Dynamic phase diagrams of the Blume-Capel model in an oscillating field by the path probability method

TL;DR

This paper investigates the dynamic phase transitions of the Blume-Capel model under oscillating magnetic fields using the path probability method, revealing complex phase diagrams with tricritical and reentrant behaviors.

Contribution

It introduces the application of the path probability method to analyze dynamic phase diagrams of the Blume-Capel model under time-dependent fields, highlighting novel phase behaviors.

Findings

Identification of paramagnetic, ferromagnetic, and mixed phases.

Discovery of tricritical, reentrant, and multi-critical points.

Comparison with Glauber-type stochastic dynamics results.

Abstract

We calculate the dynamic phase transition (DPT) temperatures and present the dynamic phase diagrams in the Blume-Capel model under the presence of a time-dependent oscillating external magnetic field by using the path probability method. We study the time variation of the average order parameters to obtain the phases in the system and the paramagnetic (P), ferromagnetic (F) and the F + P mixed phases are found. We also investigate the thermal behavior of the dynamic order parameters to analyze the nature (continuous and discontinuous) of transitions and to obtain the DPT points. We present the dynamic phase diagrams in three planes, namely (T, h), (d, T) and (k2/k1, T), where T is the reduced temperature, h the reduced magnetic field amplitude, d the reduced crystal-field interaction and the k2, k1 rate constants. The phase diagrams exhibit dynamic tricritical and reentrant behaviors as well as a double critical end point and triple point, strongly depending on the values of the interaction parameters and the rate constants. We compare and discuss the dynamic phase diagrams with dynamic phase diagrams that are obtained within the Glauber-type stochastic dynamics based on the mean-field theory and the effective field theory.