aiqbench analysis
This paper uses normalizing flows, a generative ML model, as direct samplers for a statistical-physics problem, and reports that they locate phase transitions and the tricritical point about as accurately as established Monte Carlo methods. For ML readers, the useful result is a benchmark: flows avoid autocorrelation and work in the hard first-order region, but the claim of parity rests on finite-size scaling tests in one model family. Whether the approach generalizes to larger or more complex systems remains untested in this study.
The Blume-Capel Model as a $\phi^6$ Field Theory: A Monte Carlo and Flow Model Study
arXiv:2610.20982v1 Announce Type: cross Abstract: We report Monte Carlo simulations of a continuous spin variant of the Blume-Capel model. We compute the phase diagrams in the crystal-field-temperature plane, as a function of the softness of the spins. We show that normalizing flows, a class of generative models capable of direct sampling without autocorrelation, are effective samplers across the phase diagram, including in the first-order transition region and in the vicinity of the tricritical point. Finite-size scaling analyses of flow samples locate the first- and second-order transitions as well as the tricritical point with accuracy comparable to canonical and extended-ensemble Monte Carlo.
Abstract:We report Monte Carlo simulations of a continuous spin variant of the Blume-Capel model. We compute the phase diagrams in the crystal-field-temperature plane, as a function of the softness of the spins. We show that normalizing flows, a class of generative models capable of direct sampling without autocorrelation, are effective samplers across the phase diagram, including in the first-order transition region and in the vicinity of the tricritical point. Finite-size scaling analyses of flow samples locate the first- and second-order transitions as well as the tricritical point with accuracy comparable to canonical and extended-ensemble Monte Carlo.
Statistical Mechanics (cond-mat.stat-mech); Disordered Systems and Neural Networks (cond-mat.dis-nn); Machine Learning (cs.LG); High Energy Physics - Lattice (hep-lat)
arXiv:2610.20982 [cond-mat.stat-mech]
(or arXiv:2610.20982v1 [cond-mat.stat-mech] for this version)
https://doi.org/10.48550/arXiv.2610.20982 arXiv-issued DOI via DataCite (pending registration)
Full text under the publisher's open licence · 129 words
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