Sampling the ground-state magnetization of d-dimensional p-body Ising models

TL;DR

This paper demonstrates a heuristic algorithm's ability to uniformly sample ground states in high-degeneracy spin-glass models and uses it to analyze phase transition points in specific models.

Contribution

Introduces and validates a heuristic algorithm for sampling ground states in p-spin Ising models with high degeneracy, enabling detailed phase transition analysis.

Findings

Successfully sampled ground states in complex spin models.

Estimated critical transition points for two specific models.

Showed the algorithm's effectiveness in exploring highly degenerate ground states.

Abstract

We demonstrate that a recently introduced heuristic optimization algorithm [Phys. Rev. E 83, 046709 (2011)] that combines a local search with triadic crossover genetic updates is capable of sampling nearly uniformly among ground-state configurations in spin-glass-like Hamiltonians with p-spin interactions in d space dimensions that have highly degenerate ground states. Using this algorithm we probe the zero-temperature ferromagnet to spin-glass transition point q_c of two example models, the disordered version of the two-dimensional three-spin Baxter-Wu model [q_c = 0.1072(1)] and the three-dimensional Edwards-Anderson model [q_c = 0.2253(7)], by computing the Binder ratio of the ground-state magnetization.