Noise-to-Noise Ratios in Correlation Length Calculations Near Criticality

TL;DR

This paper introduces a novel technique using noise-to-noise ratios in variance measurements to directly calculate the correlation length and critical exponent in finite random systems, demonstrated on the random field Ising model.

Contribution

It presents a new method for determining correlation length and critical exponents directly from variance ratios, applicable across various numerical approaches.

Findings

Effective in calculating correlation length near criticality

Applicable to different numerical methods such as real space renormalization and simulation

Successfully demonstrated on the random field Ising model

Abstract

For finite random systems, it is possible to define two types of variances (noises). It is demonstrated that their ratio is useful in calculating the correlation length of an infinite and rather general random system, as a function of temperature. The numerical method of obtaining those variables is not relevant. It can be real space numerical renormalization, simulation or any other method. It does not matter. The correlation length obtained by this novel technique may then be used to obtain directly the critical correlation exponent, $\nu$, rather than indirectly, using scaling relations, as is often done. The method is demonstrated by applying it to the random field Ising model.