Analytical solution of the Monte Carlo dynamics of a simple spin-glass model
L. L. Bonilla, F. G. Padilla, G. Parisi, F. Ritort
TL;DR
This paper provides an exact analytical solution for the Monte Carlo dynamics of the spherical Sherrington-Kirkpatrick spin-glass model, revealing the precise evolution equations for moments and their relation to Langevin dynamics.
Contribution
It introduces a closed set of dynamical equations for moments in the spin-glass model, connecting Monte Carlo and Langevin dynamics in a specific limit.
Findings
Exact dynamical equations for moments derived
Energy dynamics match Langevin in a particular limit
Provides insights into spin-glass Monte Carlo behavior
Abstract
In this note we present an exact solution of the Monte Carlo dynamics of the spherical Sherrington-Kirkpatrick spin-glass model. We obtain the dynamical equations for a generalized set of moments which can be exactly closed. Only in a certain particular limit the dynamical equation of the energy coincides with that of the Langevin dynamics.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.