Fourth-Order Cumulants to Characterize the Phase Transitions of a Spin-1 Ising Model

TL;DR

This paper uses Monte Carlo simulations to analyze fourth-order cumulants of magnetization and energy, providing insights into the nature of phase transitions in a spin-1 Ising model.

Contribution

It introduces a simulation-based approach to characterize phase transitions using fourth-order cumulants in a spin-1 Ising model.

Findings

Fourth-order cumulants distinguish between first and second-order transitions.

Behavior of cumulants aligns with thermodynamic fluctuation theory.

Results enhance understanding of phase transition signatures in spin models.

Abstract

Fourth-order cumulants of physical quantities have been used to characterize the nature of a phase transition. In this paper we report some Monte Carlo simulations to illustrate the behavior of fourth-order cumulants of magnetization and energy across second and first-order transitions in the phase diagram of a well known spin-1 Ising model. Simple ideas from the theory of thermodynamic fluctuations are used to account for the behavior of these cumulants.