Two-dimensional spanning webs as (1,2) logarithmic minimal model

TL;DR

This paper studies a lattice model of critical spanning webs on a finite cylinder, revealing its connection to symplectic fermions and logarithmic conformal field theories with specific boundary conditions.

Contribution

It introduces a generalized spanning web model with cycles, linking its scaling limit partition function to symplectic fermion characters under various boundary conditions.

Findings

Partition function matches symplectic fermion characters

Model generalizes spanning trees with cycles

Results confirm logarithmic CFT behavior

Abstract

A lattice model of critical spanning webs is considered for the finite cylinder geometry. Due to the presence of cycles, the model is a generalization of the known spanning tree model which belongs to the class of logarithmic theories with central charge $c=-2$. We show that in the scaling limit the universal part of the partition function for closed boundary conditions at both edges of the cylinder coincides with the character of symplectic fermions with periodic boundary conditions and for open boundary at one edge and closed at the other coincides with the character of symplectic fermions with antiperiodic boundary conditions.