In this paper, we propose a new generalized XY model with nearest-neighbor interaction which cannot be studied analytically. By adopting both the canonical Monte Carlo simulations and the microcanonical Monte Carlo simulations, the first-order phase transitions in both canonical ensemble and microcanonical ensemble are observed numerically, and the accurate phase-transition temperatures of the model with different parameters are given. From the distinct phase diagrams in two different ensembles, we conclude that the model we propose here exists as an ensemble equivalence.In this paper, we propose a new generalized XY model with nearest-neighbor interaction which cannot be studied analytically. By adopting both the canonical Monte Carlo simulations and the microcanonical Monte Carlo simulations, the first-order phase transitions in both canonical ensemble and microcanonical ensemble are observed numerically, and the accurate phase-transition temperatures of the model with different parameters are given. From the distinct phase diagrams in two different ensembles, we conclude that the model we propose here exists as an ensemble equivalence.

Modern Physics Letters BJan 10, 20231 citation

First order phase transitions in the canonical and the microcanonical ensemble

Alfred H�ller

The European Physical Journal BSep 1, 199473 citations

Gaussian Ensemble as an Interpolating Ensemble

Murty S. S. Challa, J. H. Hetherington

We consider a noncanonical ensemble which involves a sample thermally connected to a finite heat bath with specific properties. Treating the size of the heat bath as a parameter, we show that static properties of finite samples are ensemble dependent. Monte Carlo simulations of phase transitions in Potts models confirm the analysis and demonstrate significant reductions in computer time (sometimes by a factor of 100) compared to canonical-ensemble simulations. For finite samples, second-order transitions are sharpened and are clearly distinguished from first-order transitions as the heat bath becomes smaller.We consider a noncanonical ensemble which involves a sample thermally connected to a finite heat bath with specific properties. Treating the size of the heat bath as a parameter, we show that static properties of finite samples are ensemble dependent. Monte Carlo simulations of phase transitions in Potts models confirm the analysis and demonstrate significant reductions in computer time (sometimes by a factor of 100) compared to canonical-ensemble simulations. For finite samples, second-order transitions are sharpened and are clearly distinguished from first-order transitions as the heat bath becomes smaller.

Physical Review LettersJan 11, 198886 citations

Monte Carlo investigation of the influence of randomness at first-order phase transitions

Bertrand Berche, Christophe Chatelain

Computer Physics CommunicationsSep 1, 19990 citations

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

Ejaaz Merali, Ryan Larson, Ehsan Khatami +1 more

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.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.

arXiv:2610.20982Oct 14, 20260 citations

The Monte Carlo method for the study of phase transitions: A review of some recent progress

Kurt Binder

Journal of Computational PhysicsMay 1, 1985132 citations

The Blume-Capel Model as a

ϕ^6

Field Theory: A Monte Carlo and Flow Model Study