Finite-size corrections for universal boundary entropy in bond percolation

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 $L$. 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.

arXiv comment30 pages, 8 figures

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Cited by in corpus (5)

• Universal terms in the overlap of the ground state of the spin-1/2 XXZ chain with the Néel state
• Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder
• On the logarithmic bipartite fidelity of the open XXZ spin chain at $\Delta =-1/2$
• Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder II: rotated lattice
• The open XXZ chain at $\Delta =-1/2$ and the boundary quantum Knizhnik-Zamolodchikov equations