Circumventing spin glass traps by microcanonical spontaneous symmetry breaking
This addresses the challenge of efficiently navigating complex energy landscapes in statistical physics and optimization, though it appears incremental as it builds on known models and methods.
The paper tackles the problem of spin glass traps blocking simulated annealing in planted p-spin interaction models by demonstrating that a microcanonical polarized phase dominates at intermediate energies, enabling avoidance of these traps with a restart strategy, achieving exponential dominance and a discontinuous transition.
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.