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

TL;DR

This paper presents high-precision Monte Carlo simulations of a large 2D Ising model with impurities, revealing that the critical spin-spin correlation function closely resembles that of a pure system despite a significantly reduced critical temperature.

Contribution

It provides detailed numerical analysis of impurity effects on the critical correlation function in a large 2D Ising model, highlighting the similarity to pure system behavior.

Findings

Correlation function at criticality is nearly identical to pure system

Critical temperature with impurities is approximately half of that of pure system

Finite size and impurity effects on correlation function are characterized

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 $T_c$. Finite corrections to the correlation function due to combined action of impurities and finite lattice size are described.