Low-Temperature Sampling via Equilibrium Disagreements
Abstract
We develop a new framework for sampling at low temperatures using Glauber dynamics. In this regime, the coexistence of competing modes (commonly referred to as phases) creates bottlenecks that can make worst-case mixing exponentially slow. The main new ingredient in our framework is to relate convergence within a phase to the geometry of disagreements between two independent configurations drawn from that phase. As applications of our approach, we consider three canonical models on random regular graphs that have been central to low-temperature sampling, and establish fast convergence from natural initialisations of Glauber dynamics for every fixed degree. We show: --- For the hard-core model on random bipartite d-regular graphs, Glauber dynamics initialised from either one-sided independent set mixes within the corresponding phase in n3/2+o(1) steps throughout the non-uniqueness regime λ>λc(d). --- For the random-cluster model on random d-regular graphs, for every real q>2, Glauber dynamics initialised from the all-in edge set mixes within the ordered phase in n3/2+o(1) steps for all β≥ βc. Similarly, Glauber dynamics initialised from the all-out edge set mixes within the disordered phase in n3/2+o(1) steps for β≤ βc. --- For the ferromagnetic Ising model on random d-regular graphs, Glauber dynamics initialised from all-plus or all-minus mixes within the corresponding phase in n3/2+o(1) steps throughout the low-temperature regime β>βc(d). We also give an n2+o(1)-time algorithm that combines phase samples into samples from the full distribution, avoiding in particular time-costly approximations of the corresponding partition functions to the target sampling accuracy.
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BibTeX
@misc{galanis2026lowtemperature,
title = {{Low-Temperature Sampling via Equilibrium Disagreements}},
author = {Andreas Galanis and Daniel Stefankovic},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08416},
eprint = {2611.08416},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08416},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Low-Temperature Sampling via Equilibrium Disagreements
AU - Andreas Galanis
AU - Daniel Stefankovic
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08416
UR - https://arxiv.org/abs/2611.08416
AB - We develop a new framework for sampling at low temperatures using Glauber dynamics. In this regime, the coexistence of competing modes (commonly referred to as phases) creates bottlenecks that can make worst-case mixing exponentially slow. The main new ingredient in our framework is to relate convergence within a phase to the geometry of disagreements between two independent configurations drawn from that phase. As applications of our approach, we consider three canonical models on random regular graphs that have been central to low-temperature sampling, and establish fast convergence from natural initialisations of Glauber dynamics for every fixed degree. We show: --- For the hard-core model on random bipartite d-regular graphs, Glauber dynamics initialised from either one-sided independent set mixes within the corresponding phase in n^3/2+o(1) steps throughout the non-uniqueness regime λ>λ_c(d). --- For the random-cluster model on random d-regular graphs, for every real q>2, Glauber dynamics initialised from the all-in edge set mixes within the ordered phase in n^3/2+o(1) steps for all β≥ β_c. Similarly, Glauber dynamics initialised from the all-out edge set mixes within the disordered phase in n^3/2+o(1) steps for β≤ β_c. --- For the ferromagnetic Ising model on random d-regular graphs, Glauber dynamics initialised from all-plus or all-minus mixes within the corresponding phase in n^3/2+o(1) steps throughout the low-temperature regime β>β_c(d). We also give an n^2+o(1)-time algorithm that combines phase samples into samples from the full distribution, avoiding in particular time-costly approximations of the corresponding partition functions to the target sampling accuracy.
ER -