Optimizing glassy p-spin models

TL;DR

This paper demonstrates that finding ground states in p-spin models with p=3 is NP-hard even in two dimensions and introduces algorithms capable of solving large instances with high confidence.

Contribution

It establishes the NP-hardness of 3-spin models in 2D and provides new exact and heuristic algorithms for large-scale ground state computation.

Findings

NP-hardness of 3-spin models in 2D established

Algorithms successfully solve large systems of up to several thousand spins

Ground states can be found with high confidence using the proposed methods

Abstract

Computing the ground state of Ising spin-glass models with p-spin interactions is, in general, an NP-hard problem. In this work we show that unlike in the case of the standard Ising spin glass with two-spin interactions, computing ground states with p=3 is an NP-hard problem even in two space dimensions. Furthermore, we present generic exact and heuristic algorithms for finding ground states of p-spin models with high confidence for systems of up to several thousand spins.