Synchronous and asynchronous Monte Carlo dynamics of mean-field spin glasses with rotationally invariant couplings: what they share and where they differ
Abstract
We compare two Markov chain Monte Carlo dynamics for Ising spin glasses with rotationally invariant couplings: the synchronous Monte Carlo method (SyncMC), which updates all spins in parallel with the help of Gaussian auxiliary fields, and asynchronous Metropolis-Hastings dynamics, which updates one spin at a time. Using the Guionnet-Maïda formula, we derive the dynamical mean-field theory of both dynamics in terms of the R-transform of the coupling spectrum. The two effective single-spin processes share a retarded self-interaction and a Gaussian noise; SyncMC has, in addition, an instantaneous self-coupling and a noise that depends only on the response function. These additional terms act only on the fastest time scale, so that the equations for slow time scales, including the fluctuation-dissipation ratio and, for the Sherrington-Kirkpatrick model, the Parisi equation, are the same for the two dynamics. Simulations of the random orthogonal and Sherrington-Kirkpatrick models confirm that both dynamics approach the same fluctuation-dissipation relations, differing only in how many updates they need to do so.
Related
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BibTeX
@misc{kabashima2026synchronous,
title = {{Synchronous and asynchronous Monte Carlo dynamics of mean-field spin glasses with rotationally invariant couplings: what they share and where they differ}},
author = {Yoshiyuki Kabashima},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24942},
eprint = {2610.24942},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24942},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Synchronous and asynchronous Monte Carlo dynamics of mean-field spin glasses with rotationally invariant couplings: what they share and where they differ
AU - Yoshiyuki Kabashima
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.24942
UR - https://arxiv.org/abs/2610.24942
AB - We compare two Markov chain Monte Carlo dynamics for Ising spin glasses with rotationally invariant couplings: the synchronous Monte Carlo method (SyncMC), which updates all spins in parallel with the help of Gaussian auxiliary fields, and asynchronous Metropolis-Hastings dynamics, which updates one spin at a time. Using the Guionnet-Maïda formula, we derive the dynamical mean-field theory of both dynamics in terms of the R-transform of the coupling spectrum. The two effective single-spin processes share a retarded self-interaction and a Gaussian noise; SyncMC has, in addition, an instantaneous self-coupling and a noise that depends only on the response function. These additional terms act only on the fastest time scale, so that the equations for slow time scales, including the fluctuation-dissipation ratio and, for the Sherrington-Kirkpatrick model, the Parisi equation, are the same for the two dynamics. Simulations of the random orthogonal and Sherrington-Kirkpatrick models confirm that both dynamics approach the same fluctuation-dissipation relations, differing only in how many updates they need to do so.
ER -