The random anisotropy model revisited

TL;DR

This paper investigates the thermodynamic properties and phase diagram of the large-N limit of the random-anisotropy O(N) model at zero temperature, clarifying its critical behavior and glassy phases.

Contribution

It provides a unified analysis connecting Schwinger-Dyson equations and the functional renormalization group for the model.

Findings

Unified phase diagram and critical behavior description

Clarification of the nature of glassy phases

Implications for finite-N and finite-temperature systems

Abstract

We revisit the thermodynamic behavior of the random-anisotropy O($N$) model by investigating its large-$N$ limit. We focus on the system at zero temperature where the mean-field-like artifacts of the large-$N$ limit are less severe. We analyze the connection between the description in terms of self-consistent Schwinger-Dyson equations and the functional renormalization group. We provide a unified description of the phase diagram and critical behavior of the model and clarify the nature of the possible "glassy" phases. Finally we discuss the implications of our findings for the finite-$N$ and finite-temperature systems.