Pseudo Transitions in the Finite-Size Blume-Capel Model

TL;DR

This study explores pseudo phase transitions in the finite-size Blume-Capel model using advanced sampling methods, revealing the nature and order of transitions and extending the phase diagram.

Contribution

It introduces a combined microcanonical and canonical analysis approach to identify and characterize higher-order phase transitions in the finite-size Blume-Capel model.

Findings

No third-order transition beyond the tricritical point for D > 1.965

Discovery of a fourth-order independent transition at high temperature

Confirmation of phase transition from ordered to disordered paramagnetic phases

Abstract

This article investigates the pseudo transitions of the Blume-Capel model on two-dimensional finite-size lattices. By employing the Wang-Landau sampling method and microcanonical inflection point analysis, we identified the positions of phase transitions as well as higher-order phase transitions. Through Metropolis sampling and canonical ensemble analysis, we determined the geometric characteristics of the system at these transition points. When the crystal field parameter $D$ exceeds 1.965, crossing the tricritical point, no third-order dependent phase transition is observed. However, a fourth-order independent transition was identified in the high-temperature region, and through Metropolis sampling analysis, a phase transition from the ordered paramagnetic phase to the disordered paramagnetic phase was confirmed, enhancing the phase diagram. Furthermore, the positions of the third-order phase transition obtained from both microcanonical and canonical analyses are consistent and mutually corroborative. We speculate that third-order dependent transitions vanish in the presence of strong first-order phase transitions.