Geometrical mutual information at the tricritical point of the two-dimensional Blume-Capel model

TL;DR

This paper uses Monte Carlo simulations and the Geometrical Mutual Information to estimate the central charge at the tricritical point of the 2D Blume-Capel model, confirming the theoretical value and locating the tricritical point.

Contribution

It introduces a GMI-based method to numerically identify the tricritical point in the phase diagram of the 2D Blume-Capel model.

Findings

Estimated the central charge c ≈ 0.7 near the tricritical point.

Validated the GMI approach by matching the known CFT value.

Provided a numerical method to locate the tricritical point.

Abstract

The spin-1 classical Blume-Capel model on a square lattice is known to exhibit a finite-temperature phase transition described by the tricritical Ising CFT in 1+1 space-time dimensions. This phase transition can be accessed with classical Monte Carlo simulations, which, via a replica-trick calculation, can be used to study the shape-dependence of the classical R\'enyi entropies for a torus divided into two cylinders. From the second R\'enyi entropy, we calculate the Geometrical Mutual Information (GMI) introduced by St\'ephan et. al. [Phys. Rev. Lett. 112, 127204 (2014)] and use it to extract a numerical estimate for the value of the central charge near the tricritical point. By comparing to the known CFT result, $c=7/10$, we demonstrate how this type of GMI calculation can be used to estimate the position of the tricritical point in the phase diagram.