THE SPIN-S BLUME-CAPEL RG FLOW DIAGRAM

TL;DR

This paper uses Finite Size Scaling Renormalisation Group to analyze the phase diagram of the Blume-Capel model for spins 1 and 3/2, revealing differences from mean field predictions especially for S=3/2.

Contribution

It provides the two-dimensional flow diagram of the Blume-Capel model for S=1 and S=3/2, highlighting discrepancies with mean field theory for the higher spin case.

Findings

For S=1, results align with mean field theory, showing first and second order transitions with a tricritical point.

For S=3/2, results differ from mean field predictions, showing a multicritical point instead of a critical end point.

The study demonstrates the effectiveness of Finite Size Scaling Renormalisation Group in analyzing complex phase diagrams.

Abstract

Using the Finite Size Scaling Renormalisation Group we obtain the two-dimensional flow diagram of the Blume-Capel model, for S = 1 and S = 3/2. In the first case our results are similar to those of Mean Field Theory, which predicts the existence of first and second order transitions whith a tricritical point. In the second case, however, our results are different. While we obtain, as in the S = 1 case, a phase diagram presenting a multicritical point, the Mean Field approach predicts only a second order transition and a critical end point.