Full reduction of large finite random Ising systems by RSRG

TL;DR

This paper introduces a renormalization approach to efficiently evaluate physical quantities in large finite random Ising systems, enabling detailed analysis of correlations and critical behavior.

Contribution

It presents a novel renormalization method that reduces system complexity, allowing direct calculation of correlations, susceptibility, and critical exponents in 3D random Ising models.

Findings

First full 3D correlation calculation in this context

Accurate determination of critical temperature and exponents

Numerical results for susceptibility and correlation functions

Abstract

We describe how to evaluate approximately various physical interesting quantities in random Ising systems by direct renormalization of a finite system. The renormalization procedure is used to reduce the number of degrees of freedom to a number that is small enough, enabling direct summing over the surviving spins. This procedure can be used to obtain averages of functions of the surviving spins. We show how to evaluate averages that involve spins that do not survive the renormalization procedure. We show, for the random field Ising model, how to obtain the "connected" 2-spin correlation function and the "disconnected" 2-spin correlation function. Consequently, we show how to obtain the average susceptibility and the average energy. For an Ising system with random bonds and random fields we show how to obtain the average specific heat. We conclude by presenting our numerical results for the average susceptibility and the "connected" 2-spin correlation function along one of the principal axes. (We believe this to be the first time, where the full three dimensional correlation is calculated and not just parameters like Nu or Eta.) The results for the average susceptibility are used to extract the critical temperature and critical exponents of the 3D random field Ising system.