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.
Cited by 2
Jesper Lykke Jacobsen et al., Bootstrap approach to geometrical four-point functions in the two-dimensional critical Q-state Potts model: a study of the s-channel spectra
J. High Energ. Phys. 2019, 84 (2019) [Crossref]
Michael Brockmann et al., Universal terms in the overlap of the ground state of the spin-1/2 XXZ chain with the Néel state
J. Phys. A: Math. Theor. 50, 354001 (2017) [Crossref]