Geometrical mutual information at the tricritical point of the two-dimensional Blume–Capel model. (21st July 2016)

• Record Type: Journal Article
• Authors: Mandal, Ipsita; Inglis, Stephen; Melko, Roger G
• Is Part Of: Journal of statistical mechanics. (2016:Jul.)
• Publication Date: 2016-07-21
• Subjects: Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2016/07/073105
• Languages: English
• ISSNs: 1742-5468

Abstract

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 (2014 Phys. Rev. Lett .112 127204 ) 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.