Random field spin models beyond one loop: a mechanism for decreasing the lower critical dimension

TL;DR

This paper uses two-loop functional renormalization group analysis to explore the lower critical dimension in random field and anisotropy O(N) models, revealing new fixed points and phases.

Contribution

It extends the understanding of critical dimensions in random field models by calculating two-loop corrections and identifying novel fixed points for N below a critical value.

Findings

Lower critical dimension drops below 4 for N < N_c.

Discovery of a new fixed point describing the F/D transition.

Identification of a glassy regime at large N.

Abstract

The functional RG for the random field and random anisotropy O(N) sigma-models is studied to two loop. The ferromagnetic/disordered (F/D) transition fixed point is found to next order in d=4+epsilon for N > N_c (N_c=2.8347408 for random field, N_c=9.44121 for random anisotropy). For N < N_c the lower critical dimension plunges below d=4: we find two fixed points, one describing the quasi-ordered phase, the other is novel and describes the F/D transition. The lower critical dimension can be obtained in an (N_c-N)-expansion. The theory is also analyzed at large N and a glassy regime is found.