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arXiv · 2610.20982

The Blume-Capel Model as a $ϕ^6$ Field Theory: A Monte Carlo and Flow Model Study

Ejaaz Merali·Ryan Larson·Ehsan Khatami·Richard T. Scalettar
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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.

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Ejaaz Merali, Ryan Larson, Ehsan Khatami, Richard T. Scalettar. 2026-10-14. The Blume-Capel Model as a $ϕ^6$ Field Theory: A Monte Carlo and Flow Model Study. https://arxiv.org/abs/2610.20982

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