[講演者] : 藪中俊介氏（京大）

[日時] 8 月03日 14:45-

[場所] 14-213 (新棟DR3)

[タイトル]：Surprises in O(N) models: Nonperturbative fixed points, large N limits, and multicriticality

[アブストラクト]：

It is by now widely believed that everything is known about the criticality of the O(N) models either exactly

or with an accuracy that is limited only by our finite computational ability. For the Wilson-Fisher fixed point,

almost all the theoretical formalisms have been tested and they all yield consistent result.

However, for the multicritical fixed points, the situation is less clear. For example, a nontrivial multicritical

fixed point with two unstable directions branches from the Gaussian fixed point at d=3 dimension, below which

(¥phi^2)^3 term becomes relevant. The same scenario also repeats in each critical dimension d_n=2+2/n: a nontrivial

multicritical fixed point with n unstable directions branches from the Gaussian fixed point. However, in the

large N limit, only the gaussian and WF fixed points have been found in generic dimension 2<d<4 so far.

In this study, we investigate the multicritical fixed point structure of the O(N) models by means of

nonperturbative (also called functional) renormalization group (NPRG) and find some surprising features.

In particular, we find new nonperturbative fixed points in three dimensions (d=3). [1]

These fixed points come together with an intricate double-valued structure when they are considered as

functions of d and N. Many features found for the O(N) models are shared by the O(N)\otimesO(2) models relevant

to frustrated magnetic systems.

If time allows, I talk about our recent analysis of nonperturbative fixed points at N=\infty and discuss how conventional Large-N analysis breaks down for them because of the cusp-like singularities of the effective potential. [2]

[1] S. Yabunaka and B. Delamotte, Phys. Rev. Lett. (2017).

[2] S. Yabunaka and B. Delamotte, in preparation.