Correlation functions of quenched and annealed Ising systems

TL;DR

This paper calculates spin correlation functions in disordered Ising models using a two-site cluster approximation, providing exact results for 1D systems and exploring effects of long-range interactions.

Contribution

It introduces a two-site cluster approximation method for disordered Ising models, accurately capturing correlation functions in one dimension and incorporating long-range interactions.

Findings

Exact correlation functions for 1D systems

Effective inclusion of long-range interactions via mean field

Comparison between quenched and annealed disorder effects

Abstract

Spin correlation functions (up to the 3-site one) of disordered Ising model with the nearest neighbour interaction are calculated and investigated within a two-site cluster approximation for both quenched and annealed cases. The approach yields the exact results for the one-dimensional system. The long-range interaction is taken into account in the mean field approximation.