Circumventing spin glass traps by microcanonical spontaneous symmetry breaking

TL;DR

This paper introduces a microcanonical approach to avoid spin glass traps in the planted p-spin model by exploiting a spontaneous symmetry breaking transition, improving the efficiency of finding ground states.

Contribution

The study reveals a microcanonical polarized phase and a discontinuous symmetry breaking transition that can bypass spin glass traps, with an innovative restart strategy and an unsupervised learning method for ground state inference.

Findings

Microcanonical polarized phase dominates at intermediate energies.

Discontinuous symmetry breaking transition avoids spin glass traps.

Restart strategy accelerates the symmetry breaking process.

Abstract

The planted p-spin interaction model is a paradigm of random-graph systems possessing both a ferromagnetic phase and a disordered phase with the latter splitting into many spin glass states at low temperatures. Conventional simulated annealing dynamics is easily blocked by these low-energy spin glass states. Here we demonstrate that, actually this planted system is exponentially dominated by a microcanonical polarized phase at intermediate energy densities. There is a discontinuous microcanonical spontaneous symmetry breaking transition from the paramagnetic phase to the microcanonical polarized phase. This transition can serve as a mechanism to avoid all the spin glass traps, and it is accelerated by the restart strategy of microcanonical random walk. We also propose an unsupervised learning problem on microcanonically sampled configurations for inferring the planted ground state.