A dedicated algorithm for calculating ground states for the triangular random bond Ising model

TL;DR

This paper introduces an efficient polynomial-time algorithm for computing ground states of the 2D random bond Ising model on triangular lattices, enabling large-scale analysis of phase transitions.

Contribution

It presents a novel mapping of the ground state problem to a minimum-weight perfect matching problem, allowing fast computation for large 2D systems.

Findings

Analysis of the ferromagnet to spin-glass transition at T=0.

Finite-size scaling of magnetization and excitation energies.

Comparison with previous simulations and exact results.

Abstract

In the presented article we present an algorithm for the computation of ground state spin configurations for the 2d random bond Ising model on planar triangular lattice graphs. Therefore, it is explained how the respective ground state problem can be mapped to an auxiliary minimum-weight perfect matching problem, solvable in polynomial time. Consequently, the ground state properties as well as minimum-energy domain wall (MEDW) excitations for very large 2d systems, e.g. lattice graphs with up to N=384x384 spins, can be analyzed very fast. Here, we investigate the critical behavior of the corresponding T=0 ferromagnet to spin-glass transition, signaled by a breakdown of the magnetization, using finite-size scaling analyses of the magnetization and MEDW excitation energy and we contrast our numerical results with previous simulations and presumably exact results.