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

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.