Jan de Gier, Jesper Lykke Jacobsen, Anita Ponsaing
SciPost Phys. 1, 012 (2016) ·
published 19 December 2016
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 $L$. 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.
Dr Ponsaing: "Thank you for your kind commen..."
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