Static and dynamic structure factors in three-dimensional randomly diluted Ising models

TL;DR

This study investigates the critical behavior of static and dynamic structure factors in a three-dimensional randomly diluted Ising model, revealing that disorder significantly alters the dynamic decay rates while static properties remain similar to pure systems.

Contribution

It provides new insights into how disorder affects dynamic critical behavior, especially the momentum-independent decay rate in the dynamic structure factor.

Findings

Static structure factor behavior similar to pure Ising models

Dynamic structure factor exhibits momentum-independent decay rate

Disorder-induced breaking of translational invariance affects dynamics

Abstract

We consider the three-dimensional randomly diluted Ising model and study the critical behavior of the static and dynamic spin-spin correlation functions (static and dynamic structure factors) at the paramagnetic-ferromagnetic transition in the high-temperature phase. We consider a purely relaxational dynamics without conservation laws, the so-called model A. We present Monte Carlo simulations and perturbative field-theoretical calculations. While the critical behavior of the static structure factor is quite similar to that occurring in pure Ising systems, the dynamic structure factor shows a substantially different critical behavior. In particular, the dynamic correlation function shows a large-time decay rate which is momentum independent. This effect is not related to the presence of the Griffiths tail, which is expected to be irrelevant in the critical limit, but rather to the breaking of translational invariance, which occurs for any sample and which, at the critical point, is not recovered even after the disorder average.