First Order Phase Transition in the 3-dimensional Blume-Capel Model on a Cellular Automaton

TL;DR

This paper investigates the first order phase transition in the 3D Blume-Capel model using an improved cellular automaton algorithm, analyzing finite-size effects and histograms to identify transition characteristics.

Contribution

It introduces an enhanced cellular automaton method to study first order phase transitions in the 3D Blume-Capel model at a specific parameter value.

Findings

Magnetic susceptibility maxima increase with system volume.

Specific heat maxima increase with system volume.

Finite-size effects confirm first order transition behavior.

Abstract

The first order phase transition of the three-dimensional Blume Capel are investigated using cooling algorithm which improved from Creutz Cellular Automaton for the $D/J=2.9$ parameter value in the first order phase transition region. The analysis of the data using the finite-size effect and the histogram technique indicate that the magnetic susceptibility maxima and the specific heat maxima increase with the system volume ($L^{d}$) at $% D/J=2.9$.