The Critical Behaviour of the Spin-3/2 Blume-Capel Model in Two Dimensions

TL;DR

This study investigates the phase transitions of the two-dimensional spin-3/2 Blume-Capel model using simulations and theoretical analysis, revealing the absence of a multicritical point and comparing classical and quantum versions.

Contribution

The paper provides a detailed analysis of the phase diagram of the 2D spin-3/2 Blume-Capel model, clarifying the nature of its critical points and contrasting with prior theoretical predictions.

Findings

No multicritical point along the transition line.

Qualitative agreement with mean field predictions.

Disagreement with previous renormalization group results.

Abstract

The phase diagram of the spin-3/2 Blume-Capel model in two dimensions is explored by conventional finite-size scaling, conformal invariance and Monte Carlo simulations. The model in its $\tau$-continuum Hamiltonian version is also considered and compared with others spin-3/2 quantum chains. Our results indicate that differently from the standard spin-1 Blume-Capel model there is no multicritical point along the order-disorder transition line. This is in qualitative agreement with mean field prediction but in disagreement with previous approximate renormalization group calculations. We also presented new results for the spin-1 Blume-Capel model.