NEW TOPOLOGIES IN THE PHASE DIAGRAM OF THE SEMI-INFINITE BLUME-CAPEL MODEL

TL;DR

This paper explores new topologies in the phase diagram of the semi-infinite Blume-Capel model, revealing two novel phases and demonstrating improved accuracy over mean field methods through cluster variation and low temperature expansion techniques.

Contribution

It introduces two new phase topologies in the Blume-Capel model's phase diagram and compares cluster variation results with low temperature expansion for enhanced accuracy.

Findings

Discovery of two new phase topologies.

Identification of a new phase with distinct surface order.

Enhanced accuracy over mean field approximation.

Abstract

The phase diagram of the Blume--Capel model on a semi--infinite simple cubic lattice with a (100) free surface is studied in the pair approximation of the cluster variation method. Six main topologies are found, of which two are new, due to the occurrence of a first order surface transition in the phase with ordered bulk, separating two phases with large and small surface order parameters. The latter is a new phase and is studied in some detail, giving the behaviour of the order parameter profiles in two typical cases. A comparison is made with the results of a low temperature expansion, where these are available, showing a great increase in accuracy with respect to the mean field approximation.