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

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 Rényi entropies for a torus divided into two cylinders. From the second Rényi entropy, we calculate the Geometrical Mutual Information (GMI) introduced by Stéphan 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.

version accepted in JSTAT

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Cited by in corpus (4)

• Ising universality in the two-dimensional Blume-Capel model with quenched random crystal field
• Transfer-matrix approach to the Blume-Capel model on the triangular lattice
• Metastability in graded and step like variation of field and anisotropy of the Blume-Capel ferromagnet
• Information-Geometric Signatures from Nonextensivity in the $1$-D Blume-Capel Model