Critical and tricritical singularities from small-scale Monte Carlo simulations: The Blume-Capel model in two dimensions

TL;DR

This paper demonstrates that analyzing partition function zeros in small-scale Monte Carlo simulations of the 2D Blume-Capel model yields highly accurate insights into its critical and tricritical behaviors, surpassing traditional finite-size scaling methods.

Contribution

It introduces a zeros analysis approach for small systems that accurately determines critical properties of the 2D Blume-Capel model, highlighting its sensitivity and precision.

Findings

Zeros analysis achieves high accuracy even for small systems.

The method detects subtle crossover effects.

Zeros are highly sensitive to critical phenomena.

Abstract

We show that the study of critical properties of the Blume-Capel model at two dimensions can be deduced from Monte Carlo simulations with good accuracy even for small system sizes when one analyses the behaviour of the zeros of the partition function. The phase diagram of the model displays a line of second-order phase transitions ending at a tricritical point, then a line of first-order transitions. We concentrate on critical and tricritical properties and compare the accuracy achieved via standard finite-size scaling of thermodynamic quantities with that from the zeros analysis. This latter analysis showcases spectacular precision, even for systems as small as 64 spins! We also show that the zeros are very sensitive to subtle crossover effects.