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

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.