The Blume-Capel Model as a $φ^6$ Field Theory: A Monte Carlo and Flow Model Study
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.
| Authors | Ejaaz Merali, Ryan Larson, Ehsan Khatami et al. |
|---|---|
| Primary category | cond-mat.stat-mech |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
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