Cluster-Exact Approximation of Spin Glass Groundstates

TL;DR

The paper introduces an approximate algorithm for finding groundstates of Ising spin glasses by iteratively selecting frustration-free spin clusters and solving them exactly, leading to low-energy configurations.

Contribution

It presents a novel cluster-exact approximation method that combines graph-theoretical solutions with iterative updates for spin glass groundstates.

Findings

Estimated groundstate energy density for 2D: -1.400 +/- 0.005

Estimated groundstate energy density for 3D: -1.766 +/- 0.002

Distribution of overlaps used to characterize the algorithm

Abstract

We present an algorithm which calculates groundstates of Ising spin glasses approximately. It works by randomly selecting clusters of spins which exhibit no frustrations. The spins which were not selected, contribute to the local fields of the selected spins. For the spin--cluster a groundstate is exactly calaculated by using graphtheoretical methods. The other spins remain unchanged. This procedure is repeated many times resulting in a state with low energy. The total time complexity of this scheme is approximately cubic. We estimate that the groundstate energy density of the infinite system for the +/- J model is -1.400 +/- 0.005 (2d) and -1.766 +/- 0.002 (3d). The distribution of overlaps for selected systems is calculated in order to characterize the algorithm.