Power-law correlations and orientational glass in random-field Heisenberg models

TL;DR

This study uses Monte Carlo simulations to explore phase transitions and power-law correlations in a random-field Heisenberg model, revealing a stable power-law correlated phase even when traditional ferromagnetic order is lost.

Contribution

It demonstrates the existence of a power-law correlated phase in a random-field Heisenberg model, extending understanding of phase behavior under disorder.

Findings

Power-law correlations decay as |k|^(-3) in the intermediate phase.

The [111] ferromagnetic phase becomes unstable at small disorder fractions.

The power-law correlated phase persists even after the disappearance of the [110] ferromagnetic phase.

Abstract

Monte Carlo simulations have been used to study a discretized Heisenberg ferromagnet (FM) in a random field on simple cubic lattices. The spin variable on each site is chosen from the twelve [110] directions. The random field has infinite strength and a random direction on a fraction x of the sites of the lattice, and is zero on the remaining sites. For x = 0 there are two phase transitions. At low temperatures there is a [110] FM phase, and at intermediate temperature there is a [111] FM phase. For x > 0 there is an intermediate phase between the paramagnet and the ferromagnet, which is characterized by a |k|^(-3) decay of two-spin correlations, but no true FM order. The [111] FM phase becomes unstable at a small value of x. At x = 1/8 the [110] FM phase has disappeared, but the power-law correlated phase survives.