Critical Point Correlation Function for the 2D Random Coupling Ising Model

TL;DR

This paper presents high-precision Monte Carlo simulations of a large 2D Ising model with impurities, revealing that its critical correlation function closely resembles that of a pure system despite significant differences in critical temperature.

Contribution

It provides detailed numerical analysis of impurity effects on the 2D Ising model's critical correlations, challenging existing theories about impurity influence.

Findings

Critical correlation functions are nearly identical to pure system.

Critical temperature with impurities is nearly half of that of the pure system.

Results contradict some competing theoretical predictions.

Abstract

High accuracy Monte Carlo simulation results for 1024*1024 Ising system with ferromagnetic impurity bonds are presented. Spin-spin correlation function at a critical point is found to be numerically very close to that of a pure system. This is not trivial since a critical temperature for the system with impurities is almost two times lower than pure Ising $T_c$. Small deviations from the pure behaviour contradict to some of the competing theories.