Bond-Propagation Algorithm for Thermodynamic Functions in General 2D Ising Models

TL;DR

This paper extends the bond propagation algorithm to directly compute thermodynamic functions in 2D Ising models, enhancing efficiency near critical points and exploring its relation to other algorithms.

Contribution

The paper introduces a method to calculate thermodynamic functions directly using bond propagation, expanding its applicability to derivatives of the partition function.

Findings

Algorithm efficiently computes thermodynamic functions in 2D Ising models.

Explicit expressions derived for derivatives of the partition function.

Discussion of algorithm relations and potential extensions to other models.

Abstract

Recently, we developed and implemented the bond propagation algorithm for calculating the partition function and correlation functions of random bond Ising models in two dimensions. The algorithm is the fastest available for calculating these quantities near the percolation threshold. In this paper, we show how to extend the bond propagation algorithm to directly calculate thermodynamic functions by applying the algorithm to derivatives of the partition function, and we derive explicit expressions for this transformation. We also discuss variations of the original bond propagation procedure within the larger context of Y-Delta-Y-reducibility and discuss the relation of this class of algorithm to other algorithms developed for Ising systems. We conclude with a discussion on the outlook for applying similar algorithms to other models.