Exploring the diluted ferromagnetic p-spin model with a Cavity Master Equation

TL;DR

This paper presents a new method based on the Cavity Master Equation to efficiently analyze the dynamics of diluted ferromagnetic p-spin models, accurately capturing behavior across phase transitions and enabling exploration of the spin-glass phase.

Contribution

The paper introduces the Cavity Master Equation as a practical and accurate tool for modeling Glauber dynamics in diluted p-spin models, including low-temperature phases.

Findings

CME accurately models ferromagnetic p-spin dynamics across phase transitions.

CME's computational cost is comparable to a single Monte Carlo simulation.

CME enables exploration of the low-temperature spin-glass phase.

Abstract

We introduce a new solution to Glauber multi-spin dynamics on random graphs. The solution is based on the recently introduced Cavity Master Equation (CME), a time-closure turning the in principle exact Dynamic Cavity Method into a practical method of analysis and of fast simulation. Running CME once is of comparable computational complexity as one Monte Carlo run on the same problem. We show that CME correctly models the ferromagnetic $p$-spin Glauber dynamics from high temperatures down to and below the spinoidal transition. We also show that CME allows a novel exploration of the low-temperature spin-glass phase of the model.