Phase diagram of an Ising model with competitive interactions on a Husimi tree and its disordered counterpart

TL;DR

This paper explores the phase diagram of a frustrated Ising model on a Husimi tree, revealing phase transitions including spin glass behavior, and introduces a method to analyze disordered systems via a mapping to non-random models.

Contribution

It provides a detailed phase diagram of an Ising model with frustration on a Husimi tree and extends the analysis to disordered spin glass versions using a novel mapping method.

Findings

Presence of a phase transition in the disordered model at any finite coupling

Identification of a glassy transition in frustrated regions

Application of a new method to determine phase boundaries in random models

Abstract

We consider an Ising competitive model defined over a triangular Husimi tree where loops, responsible for an explicit frustration, are even allowed. After a critical analysis of the phase diagram, in which a ``gas of non interacting dimers (or spin liquid) - ferro or antiferromagnetic ordered state'' transition is recognized in the frustrated regions, we introduce the disorder for studying the spin glass version of the model: the triangular +/- J model. We find out that, for any finite value of the averaged couplings, the model exhibits always a phase transition, even in the frustrated regions, where the transition turns out to be a glassy transition. The analysis of the random model is done by applying a recently proposed method which allows to derive the upper phase boundary of a random model through a mapping with a corresponding non random one.