A self-consistent Ornstein-Zernike approximation for the Random Field Ising model

TL;DR

This paper extends the SCOZA method to the random field Ising model, enabling analysis of phase diagrams and critical phenomena influenced by disorder distribution in finite dimensions.

Contribution

It introduces a novel approach using the replica formalism to treat quenched disorder as an annealed variable, allowing detailed study of disorder effects on phase transitions.

Findings

Accurately predicts critical temperature dependence on disorder for d>4

Identifies tricritical points for bimodal and Gaussian distributions

Shows the influence of distribution type and dimension on phase behavior

Abstract

We extend the self-consistent Ornstein-Zernike approximation (SCOZA), first formulated in the context of liquid-state theory, to the study of the random field Ising model. Within the replica formalism, we treat the quenched random field as an annealed spin variable, thereby avoiding the usual average over the random field distribution. This allows to study the influence of the distribution on the phase diagram in finite dimensions. The thermodynamics and the correlation functions are obtained as solutions of a set a coupled partial differential equations with magnetization, temperature and disorder strength as independent variables. A preliminary analysis based on high-temperature and 1/d series expansions shows that the theory can predict accurately the dependence of the critical temperature on disorder strength for dimensions d>4. For the bimodal distribution, we find a tricritical point which moves to weaker fields as the dimension is reduced. For the Gaussian distribution, a tricritical point may appear for d slightly above 4.