The Blume-Capel model for spins S=1 and 3/2 in dimensions d=2 and 3

TL;DR

This paper provides high- and low-temperature series expansions for the Blume-Capel model with spins 1 and 3/2 in 2D and 3D, analyzing critical properties across various lattice types and fields.

Contribution

It introduces detailed high- and low-temperature series expansions for the Blume-Capel model with spins 1 and 3/2, including exact coefficients as functions of fields.

Findings

Series expansions up to 24th order at high-temperature

Series expansions up to 11th order at low-temperature

Analysis of critical properties for spins 1 and 3/2

Abstract

Expansions through the 24th order at high-temperature and up to 11th order at low-temperature are derived for the main observables of the Blume-Capel model on bipartite lattices (sq, sc and bcc) in 2d and 3d with various values of the spin and in presence of a magnetic field. All expansion coefficients are computed exactly as functions of the crystal and magnetic fields. Several critical properties of the model are analyzed in the two most studied cases of spin S=1 and S=3/2.