On composite systems of dilute and dense couplings

TL;DR

This paper investigates composite Ising spin systems with both dilute and dense couplings, analyzing their thermodynamic behavior and phase transitions using the replica method and population dynamics.

Contribution

It introduces a comprehensive analysis of mixed dilute and dense coupling models, exploring their high and low temperature phases and transitions.

Findings

High temperature transition behavior varies with mixing parameter

Exact analysis of competing effects near phase transitions

Low temperature behavior characterized using replica symmetry and population dynamics

Abstract

Composite systems, where couplings are of two types, a combination of strong dilute and weak dense couplings of Ising spins, are examined through the replica method. The dilute and dense parts are considered to have independent canonical disordered or uniform bond distributions; mixing the models by variation of a parameter $\gamma$ alongside inverse temperature $\beta$ we analyse the respective thermodynamic solutions. We describe the variation in high temperature transitions as mixing occurs; in the vicinity of these transitions we exactly analyse the competing effects of the dense and sparse models. By using the replica symmetric ansatz and population dynamics we described the low temperature behaviour of mixed systems.