Phase transitions in the Blume-Capel model with trimodal and Gaussian random fields

TL;DR

This paper investigates how trimodal and Gaussian symmetric random fields influence the phase diagram of the infinite-range Blume-Capel model, revealing complex phase structures and critical phenomena.

Contribution

It provides a detailed analysis of phase transitions in the Blume-Capel model under different symmetric random field distributions, identifying new phases and critical points.

Findings

Trimodal random fields induce multiple new phases and multicritical points.

Gaussian random fields lead to a continuous transition line ending at a tricritical point.

Re-entrance phenomena occur at low temperatures for certain parameters.

Abstract

We study the effect of different symmetric random field distributions: trimodal and Gaussian on the phase diagram of the infinite range Blume-Capel model. For the trimodal random field, the model has a very rich phase diagram. We find three new ordered phases, multicritical points like tricritical point (TCP), bicritical end point (BEP), critical end point (CEP) along with some multi-phase coexistence points. We also find re-entrance at low temperatures for some values of the parameters. On the other hand for the Gaussian distribution the phase diagram consists of a continuous line of transition followed by a first order transition line, meeting at a TCP. The TCP vanishes for higher strength of the random field. In contrast to the trimodal case, in Gaussian case no new phase emerges.