Quasi-long range order in the random anisotropy Heisenberg model

TL;DR

This paper investigates the large-distance behavior of the random anisotropy and random field Heisenberg models using the functional renormalization group, revealing a phase with quasi-long-range order in the anisotropy model and finite correlation in the field model.

Contribution

It provides a detailed analysis of the phase behavior and correlation functions of the random anisotropy Heisenberg model using $4- ext{}\epsilon$ dimensional RG methods, highlighting the existence of quasi-long-range order.

Findings

Random anisotropy model exhibits a phase with infinite correlation radius at low temperatures.

Correlation function follows a power law decay with an exponent proportional to $\epsilon$.

Magnetic susceptibility diverges as a power law at low fields.

Abstract

The large distance behaviors of the random field and random anisotropy Heisenberg models are studied with the functional renormalization group in $4-\epsilon$ dimensions. The random anisotropy model is found to have a phase with the infinite correlation radius at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law $<{\bf m}({\bf r}_1) {\bf m}({\bf r}_2)>\sim| {\bf r}_1-{\bf r}_2|^{-0.62\epsilon}$. The magnetic susceptibility diverges at low fields as $\chi\sim H^{-1+0.15\epsilon}$. In the random field model the correlation radius is found to be finite at the arbitrarily weak disorder.