The Energy-Energy Correlation Function of the Random Bond Ising Model in Two Dimensions

TL;DR

This paper analyzes the energy-energy correlation function in a 2D random bond Ising model, revealing two correlation lengths with distinct behaviors and critical exponents, using an effective field theory approach.

Contribution

It introduces a novel analysis of energy correlations in the 2D random bond Ising model, highlighting the existence of two correlation lengths and their critical properties.

Findings

Two correlation lengths exist in the disordered model.

One correlation length is finite, the other diverges at criticality.

The divergent correlation length has a critical exponent of 1/2.

Abstract

The energy-energy correlation function of the two-dimensional Ising model with weakly fluctuating random bonds is evaluated in the large scale limit. Two correlation lengths exist in contrast to one correlation length in the pure 2D Ising model: one is finite whereas the other is divergent at the critical points. The corresponding exponent of the divergent correlation length is $\nu_e=1/2$ in contrast to the pure system where $\nu_e=1$. The calculation is based on a previously developed effective field theory for the energy density fluctuations.