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arXiv · 1604.02464

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

Ipsita Mandal·Stephen Inglis·Roger G. Melko
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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.

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Ipsita Mandal, Stephen Inglis, Roger G. Melko. 2016-04-08. Geometrical mutual information at the tricritical point of the two-dimensional Blume-Capel model. https://doi.org/10.1088/1742-5468/2016/07/073105

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