Critical
Phenomena &
Renormalization
Group

Conveners

Anna Hasenfratz, University of BoulderSimon Hands, University of Liverpool
Tereza Medes, University of São Paulo

General Motivation

Highlight and strengthen connections between different concepts & methods in other topics (Essentials, Algorithms, Thermodynamics, Renormalization), illustrating general topics in Statistical Mechanics (spin models, conformal transition, KT transitions and quantum transitions in general) and Complex Systems

e.g., analogy spin glasses, which are also relevant to quantum annealing and machine learning: phase diagram of QCD in the Nf plane shares similarities with that of a quantum glass in the temperature vs. magnetic field plane

How does it relate to Lattice QCD?

QCD in extreme conditions naturally introduces the notion of phase transitions (as detailed in the Thermodynamics topic), motivating an introduction to critical phenomena in statistical mechanics, including mention to RG ideas, how to use universality to get better control of things like critical exponents and general scaling properties
Continuum limit may be viewed as a critical point, with scaling and universality properties (e.g.\ invariance of the limit for different actions/discretizations, as explored in the topic of improvement) given by the RG as a consequence. Material already available in A. Hasenfratz's lectures

How is the topic divided?

Critical Behavior & Continuum Limit: Critical fluctuations, renormalisation group, scaling, universality, approach to continuum quantum field theory; overlaps with Essentials
Numerical Methods: Methodology for studying phase transitions, both first and second order: finite volume scaling, Binder cumulants, reweighting, multicanonical; overlap with Algorithms
Interesting Phase Transistions: Phenomenologically interesting phase transitions and near-critical systems, what is known, experimental/observational implications (QCD, electroweak, condensed matter); overlap with Thermodynamics

Lectures

Critical Behavior & Continuum Limit

Phase Transistions: Ising Model

Criticality, Scaling, Universality

Wilsonian RG

Applications

Library

1 Composite Higgs models

Tasi 2009 lectures: The Higgs as a Composite Nambu-Goldstone Boson – R. Contino
The Composite Nambu-Goldstone Higgs – G. Panico, A. Wulzer
Video Lectures @ICTP – A. Wulzer
Seminal papers by Kaplan, Weinberg, Georgi,...

2 Large-N

David Tong's notes on gauge theories
Coleman's "Aspects of symmetry"
Lectures on QFT by John Preskill

3 Axions

Coleman's "Aspects of symmetry"
"Theta dependence of SU(N) gauge theories in the presence of a topological term" – E. Vicari, H. Panagopoulos
Schulman's "Techniques and applications of Path integration"
Lectures on QFT by John Preskill
R. Peccei's - "The Strong CP Problem and Axions" - hep-ph/0607268