Parallel multicanonical study of the three-dimensional Blume-Capel model

TL;DR

This paper uses parallelized multicanonical simulations to explore the thermodynamics of the 3D Blume-Capel model, identifying phase transitions, universality classes, and tricritical behavior.

Contribution

It introduces a parallelized multicanonical method for studying phase transitions in the 3D Blume-Capel model across different regimes.

Findings

Determined transition points via finite-size scaling.

Verified Ising universality in the second-order regime.

Analyzed scaling near the tricritical point.

Abstract

We study the thermodynamic properties of the three-dimensional Blume-Capel model on the simple cubic lattice by means of computer simulations. In particular, we implement a parallelized variant of the multicanonical approach and perform simulations by keeping a constant temperature and crossing the phase boundary along the crystal-field axis. We obtain numerical data for several temperatures in both the first- and second-order regime of the model. Finite-size scaling analyses provide us with transition points and the dimensional scaling behavior in the numerically demanding first-order regime, as well as a clear verification of the expected Ising universality in the respective second-order regime. Finally, we discuss the scaling behavior in the vicinity of the tricritical point.