Two-point functions in boundary loop models

TL;DR

This paper derives analytical formulas for two-point functions in boundary critical loop models using conformal bootstrap, connecting continuum results with lattice data and validating with numerical simulations.

Contribution

It provides the first analytical expressions for bulk two-point functions in boundary loop models and links these to lattice quantities through universal ratios.

Findings

Analytical expressions for two-point connectivities derived.

Excellent agreement between continuum formulas and transfer-matrix numerics.

Universal ratios of amplitudes confirmed across boundary conditions.

Abstract

Using techniques of conformal bootstrap, we propose analytical expressions for a large class of two-point functions of bulk fields in critical loop models defined on the upper-half plane. Our results include the two-point connectivities in the Fortuin--Kasteleyn random cluster model with both free and wired boundary conditions. We link the continuum expressions to lattice quantities by computing universal ratios of amplitudes for the two-point connectivities, and find excellent agreement with transfer-matrix numerics.