Correlations in Random Ising Chains at Zero Temperature

TL;DR

This paper introduces a method to compute connected correlation functions in random Ising chains at zero temperature, linking them to a random walk problem, and provides exact calculations of correlation lengths for various disorder distributions.

Contribution

It presents a novel approach connecting correlation functions in disordered chains to a random walk survival probability, enabling exact correlation length calculations for different randomness types.

Findings

Correlation length is exactly calculated for various disorder distributions.

Connected correlation functions relate to the survival probability of a one-dimensional random walk.

The method applies to different random field and bond distributions.

Abstract

We present a general method to calculate the connected correlation function of random Ising chains at zero temperature. This quantity is shown to relate to the surviving probability of some one-dimensional, adsorbing random walker on a finite intervall, the size of which is controlled by the strength of the randomness. For different random field and random bond distributions the correlation length is exactly calculated.