Multicritical Behavior of Two Coupled Ising Models in the Presence of a Random Field

TL;DR

This paper explores the complex critical behavior of two coupled Ising models with a random field, revealing rich phase diagrams and transitions relevant to real systems like plastic crystals.

Contribution

It introduces a detailed analysis of coupled Ising models with random fields, uncovering diverse critical phenomena and phase transitions at various temperatures and parameters.

Findings

Rich phase diagrams with ordered, partially-ordered, and disordered phases

Sequence of phase transitions similar to plastic crystals

Model's potential to describe critical behavior in other substances

Abstract

A system defined by two coupled Ising models, with a bimodal random field acting in one of them, is investigated. The interactions among variables of each Ising system are infinite-ranged, a limit where mean field becomes exact. This model is studied at zero temperature, as well as for finite temperatures, representing physical situations which are appropriate for describing real systems, such as plastic crystals. A very rich critical behavior is found, depending directly on the particular choices of the temperature, couplings, and random-field strengths. Phase diagrams exhibiting ordered, partially-ordered, and disordered phases are analyzed, showing the sequence of transitions through all these phases, similarly to what occurs in plastic crystals. Due to the wide variety of critical phenomena presented by the model, its usefulness for describing critical behavior in other substances is also expected.