Finite-size corrections for universal boundary entropy in bond percolation

Author:

de Gier Jan1ORCID,Jacobsen Jesper234,Ponsaing Anita1ORCID

Affiliation:

1. University of Melbourne

2. CEA Saclay

3. French National Centre for Scientific Research

4. École Normale Supérieure

Abstract

We compute the boundary entropy for bond percolation on the square lattice in the presence of a boundary loop weight, and prove explicit and exact expressions on a strip and on a cylinder of size LL. For the cylinder we provide a rigorous asymptotic analysis which allows for the computation of finite-size corrections to arbitrary order. For the strip we provide exact expressions that have been verified using high-precision numerical analysis. Our rigorous and exact results corroborate an argument based on conformal field theory, in particular concerning universal logarithmic corrections for the case of the strip due to the presence of corners in the geometry. We furthermore observe a crossover at a special value of the boundary loop weight.

Funder

Australian Research Council

European Research Council

Institut Universitaire de France

Publisher

Stichting SciPost

Subject

General Physics and Astronomy

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