"Exact" Algorithm for Random-Bond Ising Models in 2D

TL;DR

The paper introduces an exact, efficient algorithm for calculating properties of 2D Ising models directly in the spin basis, capable of handling disorder and dilution with high computational efficiency.

Contribution

It presents a novel algorithm that computes exact partition functions and correlations for 2D Ising models without mapping to fermion or dimer models, improving computational efficiency.

Findings

Algorithm computes exact results in O(N^{3/2}) time for planar networks.

Efficient handling of bond/disorder and dilution, especially near percolation threshold.

Feasibility demonstrated on ferromagnetic and random-bond Ising models.

Abstract

We present an efficient algorithm for calculating the properties of Ising models in two dimensions, directly in the spin basis, without the need for mapping to fermion or dimer models. The algorithm gives numerically exact results for the partition function and correlation functions at a single temperature on any planar network of N Ising spins in O(N^{3/2}) time or less. The method can handle continuous or discrete bond disorder and is especially efficient in the case of bond or site dilution, where it executes in O(L^2 ln L) time near the percolation threshold. We demonstrate its feasibility on the ferromagnetic Ising model and the +/- J random-bond Ising model (RBIM) and discuss the regime of applicability in cases of full frustration such as the Ising antiferromagnet on a triangular lattice.