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.
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