2016/04/30 by Ipsita Mandal, Stephen Inglis, Roger G. Melko
Mathematics · Physics and Astronomy · #Condensed matter physics #Geometry #Ising model #Mathematical physics #Mathematics #Monte Carlo method #Opinion Dynamics and Social Influence #Phase (matter) #Phase diagram #Phase transition #Physics #Quantum many-body systems #Quantum mechanics #Square lattice #Statistical physics #Theoretical and Computational Physics #Torus #Tricritical point #cond-mat.stat-mech #cond-mat.str-el #hep-th #quant-ph
paper · pdf · doi:10.1088/1742-5468/2016/07/073105
published as J. Stat. Mech. (2016) 073105 · version accepted in JSTAT
arxiv created 2016/07/15 · openalex publication_date 2016/07/21 · arxiv updated 2016/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.