Ising Model on a random network with annealed or quenched disorder

TL;DR

This paper compares the equilibrium properties of an Ising model on a disordered network with quenched and annealed disorder, revealing differences in transition temperatures and entropy related to one-dimensional fluctuations.

Contribution

It provides a detailed analysis of how quenched and annealed disorder affect the thermodynamic properties of an Ising model on a complex network, using analytic and simulation methods.

Findings

Quenched disorder results in higher transition temperatures than annealed disorder.

Entropy associated with one-dimensional fluctuations is greater in quenched disorder.

Differences between quenched and annealed cases increase with disorder strength, then saturate.

Abstract

We study the equilibrium properties of an Ising model on a disordered random network where the disorder can be quenched or annealed. The network consists of four-fold coordinated sites connected via variable length one-dimensional chains. Our emphasis is on nonuniversal properties and we consider the transition temperature and other equilibrium thermodynamic properties, including those associated with one dimensional fluctuations arising from the chains. We use analytic methods in the annealed case, and a Monte Carlo simulation for the quenched disorder. Our objective is to study the difference between quenched and annealed results with a broad random distribution of interaction parameters. The former represents a situation where the time scale associated with the randomness is very long and the corresponding degrees of freedom can be viewed as frozen, while the annealed case models the situation where this is not so. We find that the transition temperature and the entropy associated with one dimensional fluctuations are always higher for quenched disorder than in the annealed case. These differences increase with the strength of the disorder up to a saturating value. We discuss our results in connection to physical systems where a broad distribution of interaction strengths is present.