Talks Abstracts

We investigate the finite-temperature properties of a bosonic Josephson junction composed of 𝑁 interacting atoms confined by a quasi one-dimensional asymmetric double-well potential, modeled by the two-site Bose-Hubbard Hamiltonian. We numerically compute the spectral decomposition of the statistical ensemble of states, the thermodynamic and entanglement entropies, the population imbalance, the quantum Fisher information, and the coherence visibility. We analyze their dependence on the system parameters, showing, in particular, how finite temperature and on-site energy asymmetry affect the entanglement and coherence properties of the system. Moreover, starting from a quantum phase model which accurately describes the system over a wide range of interactions, we develop a reliable description of the strong tunneling regime, where thermal averages may be computed analytically using a modified Boltzmann weight involving an effective temperature. We discuss the possibility of applying this effective description to other models in suitable regimes.

We build and analytically calculate the Generalised Gibbs Ensemble partition function of the integrable Soft Neumann Model. This is the model of a classical particle which is constrained to move, on average over the initial conditions, on an N dimensional sphere, and feels the effect of anisotropic harmonic potentials. We derive all relevant averaged static observables in the (thermodynamic) N → ∞ limit. We compare them to their long term dynamic averages finding excellent agreement in all phases of a non-trivial phase diagram determined by the characteristics of the initial conditions and the amount of energy injected or extracted in an instantaneous quench.

Microbial communities harbour hundreds or thousands of species whose dynamics is shaped by ecological interactions, e.g. competition and facilitation, whose empirical quantification is extremely challenging.

Alternatively, to assigning every species-level parameter, these can be chosen at random, and the dynamical states of the community studied as a function of their distribution. Application of dynamical mean field theory to random generalized Lotka-Volterra equations, a well-studied model for communities with many interacting species, thus connects emergent, community-level qualitative dynamics to a few microscopic parameters. In real systems, however, interactions are not as featureless as those represented there.

 In this talk, I will introduce interaction matrices that are the superposition of a random and a structured component, reflecting the biological knowledge at a supra-species level -- for instance the existence of functional groups, of trait-based interactions or of shared resources. A macroscopic description reflecting such a structure allows us to generalize results obtained for fully disordered communities at equilibrium.

Moreover, we explore the role of unknown sources of interaction heterogeneity on the emergent regimes of community dynamics, in particular macroscopic oscillations induced by nonlinear relations between groups of species. Within-group heterogeneity can lead each species to an equilibrium, whose stability is lost through two distinct routes: a collective phase transition, and a synchronous bifurcation of the macroscopic degrees of freedom. I will discuss the generality of the latter as a response to dispersion in microscopic time scales.

50 years ago Robert May asserted that larger and more complex ecological communities ought to be unstable. Given that large and complex ecosystems are observed, May asked what the “devious strategies” might be that nature uses to ensure stability. A decade-long "complexity-stability debate" ensued, and is ongoing.

The original work by May and much of the related recent activity in theoretical ecology is based on the analysis of spectra of random matrices. Thus, there is a direct connection to disordered systems. In the last decade or so, physicists have also contributed through the analysis of Lotka-Volterra dynamics with quenched random interaction. In these models, each species can either go extinct or survive, thus producing an emerging community. This is fundamentally different from approaches along the lines of May which usually do not specify any actual dynamics. Instead such work often starts from a hypothetical community and a hypothetical random Jacobian matrix. It is not clear if these communities are genuinely feasible equilibria of any dynamics.

In this talk, I will summarise some of the recent work on the statistical physics of random Lotka-Volterra dynamics, in particular also relating to glassy and complex behaviour. I will show that feasibility is encoded in non-Gaussian statistics of the interaction matrix. I will also demonstrate that the interactions in the surviving community constitute a non-contrived ensemble of matrices in which the universality principle of random matrix theory does not apply. That is to say that these emerging matrices have non-Gaussian features which need to be accounted for if one is to predict stability correctly. I will also discuss further properties of the surviving community, in particular in systems with hierarchical or networked interactions.

We study numerically the Hessian of low-lying minima of vector spin glass models defined on random regular graphs. We consider the two-component (XY) and three-component (Heisenberg) spin glasses at zero temperature, subjected to the action of a randomly oriented external field. Varying the intensity of the external field, these models undergo a zero temperature phase transition from a paramagnet at high field to a spin glass at low field. We study how the spectral properties of the Hessian depend on the magnetic field. In particular, we study the shape of the spectrum at low frequency and the localization properties of low-energy eigenvectors across the transition.  We find that in both phases the edge of the spectral density behaves as \lambda^{3/2}: such a behavior rules out the presence of a diverging spin-glass susceptibility 

\chi_{SG}=<\lambda^{-2}>.

As to low-energy eigenvectors, we find that the softest eigenmodes are always localized in both phases of the two models. However, by studying in detail the geometry of low-energy eigenmodes across different energy scales close to the lower edge of the spectrum, we find a different behavior for the two models at the transition: in the XY case, low-energy modes are typically localized; in the Heisenberg case low-energy eigenmodes present a multi-modal structure (a sort of ``delocalization''). These geometrically non-trivial excitations, which we call Concentrated and Delocalized Low-Energy Modes (CDLEM), coexist with trivially localized excitations: we interpret their existence as a sign of critical behavior related to the onset of the spin glass phase.

By now, there are several variants of Quantum Computing. We will focus on Quantum Computing (QC) as a natural extension of Digital Computing (DC) by using concepts and tools that should be familiar not only to Physicists but also to Computer Scientists and Mathematicians. We will quickly review them and then show how they can be combined to solve a classic problem where QC offers (potentially!) an exponential advantage compared to DC, with no need to introduce advanced topics like entanglement.

We analyze the spin glass transition in a field in finite dimension below the upper critical dimension directly at zero temperature using a recently introduced perturbative loop expansion around the Bethe lattice solution. The expansion is generated by the so-called M-layer construction. Computing analytically and numerically these non-standard diagrams at first order in the expansion, we construct an epsilon-expansion around the upper critical dimension D=8. Following standard field theoretical methods, we can find a new zero-temperature fixed-point associated with the spin glass transition in a field in dimensions D<8. We are also able to compute, at first order in the epsilon-expansion, the three independent critical exponents characterizing the transition, plus the correction-to-scaling exponent.

Complex systems tend to equilibrate slowly, exhibiting out-of-equilibrium dynamics over a broad range of timescales. A key theory challenge is to understand the features of this out-of-equilibrium behaviour from the properties of the attractors of the system’s dynamical equations. Mean-field theories of spin glass dynamics offer elegant examples of this, linking phenomena such as aging to the properties of the stationary points of the underlying free-energy landscape (which are attractors of the dynamics). However, these insights apply mainly to conservative systems. In recent years, there has been growing interest in extending these ideas to high-dimensional non-conservative systems, motivated by neural networks and theoretical ecology. In this talk, I will present a simple model of a high-dimensional system with non-reciprocal interactions, whose chaotic, out-of-equilibrium dynamics can be analyzed analytically at long times. I will discuss its dynamical phase diagram and compare it to the statistical distribution of the many, unstable equilibria of the dynamical equations. This comparison challenges the common assumption that chaotic dynamics in non-conservative settings can be understood from equilibria alone. The results rely on a combination of two analytical techniques, Dynamical Mean-Field Theory and the Kac-Rice formalism, and are presented in arXiv:2503.20908.

Many complex systems exhibit a modular structure: genomes are composed of genes, books consist of words, and technological systems like LEGO sets can be broken down into elementary building blocks. Representing these as component systems -collections of discrete elements- reveals a range of quantitative regularities, often shared across domains. Among these, Zipf’s law is perhaps the most well-known.

In this talk, I will explore some of these statistical patterns and discuss possible common generative mechanisms underlying them. I will show how simple generative models can help distinguish between "universal" patterns and system-specific features. Finally, I will argue that analyzing fluctuations around these statistical laws provides an additional layer of information, crucial for discriminating between competing generative mechanisms.

It is customary to describe biological systems as "complex," yet what we mean by complexity—and how to characterize or quantify it—often remains vague. While a comprehensive description is likely impossible, that does not mean we should not try. I will begin with an informal discussion of what complexity might entail in the context of biological systems, aiming to stimulate discussion and offer some working intuitions. I will then present two sets of data-driven findings from my research over the past two decades, focusing on systems that exhibit emergent patterns and structural regularities—what we might call biological “laws.” The first system concerns the parts lists of bacterial genomes: genes, their families, and patterns of evolutionary expansion. The second involves growing cells and how they allocate limited resources—such as ribosomes and proteins—across competing cellular processes. In both cases, I will show how relatively simple statistical models help interpret the observed patterns, revealing both features specific to biological architectures and others that resonate with widespread (universal?) properties of complex systems.

The task of sampling efficiently the Gibbs-Boltzmann distribution of disordered systems is important both for the theoretical understanding of these models and for the solution of practical optimization problems. Unfortunately, this task is known to be hard, especially for spin glasses at low temperatures. Recently, many attempts have been made to tackle the problem by mixing classical Monte Carlo schemes with newly devised Neural Networks that learn to propose smart moves. In this talk I will review a few physically-interpretable deep architectures, and in particular one whose number of parameters scales linearly with the size of the system and that can be applied to a large variety of topologies. I will show that these architectures can accurately learn the Gibbs-Boltzmann distribution for the two-dimensional and three-dimensional Edwards-Anderson models, and specifically for some of its most difficult instances. I will show that the performance increases with the number of layers, in a way that clearly connects to the correlation length of the system, thus providing a simple and interpretable criterion to choose the optimal depth. Finally, I will discuss the performances of these architectures in proposing smart Monte Carlo moves and compare to state-of-the-art algorithms. 

Reference: 

"Nearest-Neighbours Neural Network architecture for efficient sampling of statistical physics models", L.M.Del Bono, F.Ricci-Tersenghi, F.Zamponi - Machine Learning: Science and Technology 6, 025029 (2025).

Physical learning is an emerging paradigm in science and engineering whereby (meta)materials acquire desired macroscopic behaviors by exposure to examples. So far, it has been applied to static properties such as elastic moduli and self-assembled structures encoded in minima of an energy landscape. In this talk, we extend this paradigm to dynamic functionalities, such as motion and shape change, that are instead encoded in limit cycles or pathways of a dynamical system. We identify the two ingredients needed to learn time-dependent behaviors irrespective of experimental platforms: (i) learning rules with time delays and (ii) exposure to examples that break time-reversal symmetry during training. After providing a hands-on demonstration of these requirements using programmable LEGO toys, we turn to realistic particle-based simulations where the training rules are not programmed on a computer. Instead, we elucidate how they emerge from physico-chemical processes involving the causal propagation of fields, like in recent experiments on moving oil droplets with chemotactic signalling. Our trainable particles can self-assemble into structures that move or change shape on demand, either by retrieving the dynamic behavior previously seen during training, or by learning on the fly. This rich phenomenology is captured by a modified Hopfield spin model amenable to analytical treatment. The principles illustrated here provide a step towards von Neumann’s dream of engineering synthetic living systems that adapt to the environment.

The study of disordered systems has been shaped by the pioneering work of Edwards and Anderson, who introduced a minimal model to describe spin glasses and laid the foundation for understanding complex energy landscapes. Recent advances have focused on the non-equilibrium dynamics of such systems, revealing rich phenomena such as aging, slow relaxation, and memory effects. In this talk, I will discuss how disorder and frustration lead to intricate dynamical behavior in different physical (and other) systems.

• Begin at the beginning 1960s with the Kondo effect "Bandwagon"

• The localized use 1970 of the term spin glass (PWA) from magnetic glass (BC)

• First experiments using the term "spin glass" 1972

• Initial theories 1970s, theoretical/experimental explosion 1980s 

• The three-fold path of SGs in the continuing 2025 year: *Random magnetic materials, *Applications and Concepts (spin-offs) and *Off-Equilibrium Dynamics

The nature of the ordered phase of spin glasses in physical dimensions has been controversial for four decades. There is universal agreement that the Edwards-Anderson (EA) model is the appropriate model for studying this question. In the limit when the dimensionality d of the system goes to infinity, there is also universal agreement that its ordered state is that described by the Parisi replica symmetry breaking solution (RSB) of the Sherrington-Kirkpatrick (SK) model. 

This theory predicts that in the presence of an applied field there is a phase transition to a state with RSB at the de Almeida-Thouless line hAT(T). Monte Carlo simulations are very challenging in high dimensions, so we have studied the existence of such a line for the one-dimensional long-range diluted proxy model for classical Heisenberg spins and found that as d goes to 6, hAT(T)2 ~ (d − 6), implying that the nature of the ordered phase changes below six dimensions. In the one-dimensional proxy model, the probability that two spins separated by a distance r interact with each other decays as 1/r2σ. 

Tuning the exponent σ is equivalent to changing the space dimension of the short-range model Edwards-Anderson model: the relation is d = 2/(2σ − 1). The non-existence of the de Almeida-Thouless line when d < 6 has been suspected since 1980. I will briefly describe some of the non-numerical arguments which have been advanced to support its vanishing below 6 dimensions.

What then is the appropriate picture of the ordered phase of spin glasses below six dimensions in zero field and in particular for d = 3? I will argue that it is that of the droplet picture. This picture is a scaling picture which focusses on the energy of droplets of reversed spins. In the droplet picture, droplets of reversed spins have an interface fractal dimension ds < d and cost a free energy l𝜗 , where l is their linear extent. In the Parisi RSB scheme, droplets exist whose energies are of O(1) and are space-filling, that is their fractal dimension ds = d. I shall present simulational evidence that droplets of linear extent l much smaller than the system size L have droplet scaling features. However, when their linear extent l is similar to the linear size L of the system their energies and fractal nature changes to those anticipated by the RSB picture (i.e. fractal dimension ds = d and energy cost of O(1)), provided L < L*, where L* is a long length scale. In fact, Houdayer and Martin had suggested as long ago as 2000 that the droplets on the scale of the system had “sponge-like” features. The length scale L* is large in three dimensions (possibly L* > 50 lattice spacings in three dimensions and approaching infinity as d → 6), so that nearly all numerical studies have been done in the regime where L < L*. In this regime the Parisi overlap function P(q) will have features like those it has in the SK model, and I will suggest that this is a natural consequence of finite size scaling effects as in the papers of Brézin and Zinn-Justin. Only for L > L* will P(q) go over to the replica symmetric form predicted by droplet scaling.

[Work done in collaboration with Bharadwaj Vedula and Auditya Sharma, Bhopal, India]

I shall start by recalling briefly the circumstances that resulted in the papers of Edwards and Anderson and of Sherrington and Kirkpatrick. Then I shall describe some examples of pseudo-spin glasses from material situations involving atomic displacements and induction, dating back more than a decade before spin glasses but still lacking consensus. By considering minimal modelling of the latter, I shall pose some questions on the conceptual boundary between spin glasses and random fields.

Surprising signatures of anomalous spin transport have been reported in the spin-half Heisenberg spin chain at the isotropic point, in a number of recent work. The talk will discuss: (i) analogous results for classical integrable spin chains; (ii) properties of coupled KPZ equations that have been proposed as effective hydrodynamic descriptions of the integrable spin chains..

Motivated by a question about the sensitivity of knots' diffusive motion to the actual sequence of nucleotides placed on a given DNA, we discuss a simple model of such a sequence-reading diffusion on a stretched chain with a frozen sequence of “letters” A and B, having different interaction energies. The chain contains a single distortion - a “hernia" - which brings the two letters at its bottom together such that they interact. Due to interactions with the solvent, the hernia performs a random hopping motion along the chain with the transition rates dependent on its actual position. Our two focal questions are a) the dependence of various transport properties on the letters' interaction energy and b) whether these properties are self-averaging with respect to different realizations of sequences. We show that the current through a finite interval, the resistance of this interval and the splitting probabilities on this interval lack self-averaging. On the contrary, the mean first-passage time through a finite interval with N sites and the diffusion coefficient in a periodic chain are self-averaging in the asymptotic limit when N tends to infinity. Concurrently, the two latter properties exhibit significant sample-to-sample fluctuations for finite N, as evidenced by numerical simulations.

I will first discuss the equilibrium properties of a gas of N interacting particles on a line. This will include, for example, the log-gas in random matrix theory (RMT) and the Riesz gas which is a generalisation of the log-gas. I will then discuss some examples of stationary point processes that are out of equilibrium. As a simple example, I will introduce a model of N independent Brownian particles that are subjected to simultaneous stochastic resetting with rate r. The simultaneous resetting generates an effective dynamical all-to-all attractions between particles that persist even at long times in its Non-Equilibrium Stationary State (NESS). Despite the presence of strong correlations, many physical observables such as the average density, extreme statistics, order and gap/spacing statistics, full counting statistics etc. (the standard observables of interest in RMT) can be computed exactly in the NESS and they exhibit rich and interesting behaviors. The physical mechanism built in this simple model allows it to generalise and invent a whole class of solvable strongly correlated out of equilibrium point processes, some of which are experimentally realisable in optical trap systems.

Temperature chaos is a remarkable phenomenon in spin glasses, where slight changes in temperature can lead to a complete reconfiguration of the spin state. Another nontrivial phenomenon is the reentrant transition, where decreasing temperature drives the system from a ferromagnetic phase to a less-ordered spin-glass/paramagnetic phase. In this talk, I demonstrate that these physically unrelated phenomena observed in the Edwards-Anderson model are closely related mathematically. Specifically, we prove that the model exhibits temperature chaos if it has a reentrant transition, by generalizing the formulation of the problem to include correlations in the disorder variables. This work was done in collaboration with Masayuki Ohzeki and Manaka Okuyama.

Generative models, in which one trains an algorithm to generate samples ‘similar’ to those of a data base, is a major new direction developed in machine learning in the recent years. In particular, generative models based on diffusion equations have become the state of the art, notably for image generation. After an introduction to this topic, the talk will focus on the behavior of generative diffusion in the high-dimensional limit, where data are formed by a very large number of variables.  Using methods from statistical physics, and through a detailed analysis of two well-controlled high-dimensional cases, we explain the various phase transitions that take place during the dynamics of generation. Finally we discuss the use of generative diffusion to sample from glassy measures.

I will discuss how information scrambling and chaos get affected by glass transition, complex dynamics, and quantum and thermal fluctuations in paramagnetic (PM) and spin glass (SG) phases of two paradigmatic quantum spin glass models, quantum p-spin glass and Sachdev-Ye (SY) models, and in their classical limits. Our results in the classical limit of quantum p-spin glass model naturally describe chaos in supercooled liquid in structural glasses. I will show that two diagnostics of chaos, namely the Lyapunov exponent and butterfly velocity, exhibit a maximum substantially above dynamical glass transition temperature, concomitant with the crossover from simple to slow glassy relaxation. The maximum originates from enhanced chaos due to maximal complexity in the glassy landscape. I will show that the results in the p-spin glass and the SY model indicate very different evolution of glassy complexity with quantum and thermal fluctuations.

Motivated in part by magnetism-lab and Monte Carlo experiments in the 1990s, D-Wave’s superconducting quantum annealers implement a programmable transverse-field Ising model that can be quenched from a quantum paramagnetic phase to a spin glass, spin liquid, or long-range-ordered phase.  In this talk I will give an overview of the capabilities and limitations of these processors, and review recent experimental results.  These include demonstrations of quantum critical dynamics in optimization (doi.org/10.1038/s41586-023-05867-2), and simulation of fast quenches beyond the reach of classical simulation (doi.org/10.1126/science.ado6285).

In a very influential paper,  Maldacena Shenker and Stanford proved that quantum mechanics limits the level of chaos a system can have at low temperatures. Precisely this limit is reached by  models of Black Holes, giving a clear meaning to the statement that they are the most chaotic systems in the Universe. The bound on chaos works in the opposite way: when a model reaches that bound, i.e. is "as chaotic as possible" it has chances of being considered a bona fide  `toy' version of

Black Hole physics. A fact that emerges when one looks carefully into the derivation is that the bounds are intimately related to the Fluctuation-Dissipation relation, an elementary and central result of Thermodynamics.