Exact finite-size corrections and corner free energies for the c=-2 universality class

Abstract

We consider (a) the partition functions of the anisotropic dimer model on the rectangular (2M-1) x (2N-1) lattice with free and cylindrical boundary conditions with a single monomer residing on the boundary and (b) the partition function of the anisotropic spanning tree on an M x N rectangular lattice with free boundary conditions. We express (a) and (b) in terms of a principal partition function with twisted boundary conditions. Based on these expressions, we derive the exact asymptotic expansions of the free energy for both cases (a) and (b). We confirm the conformal field theory prediction for the corner free energy of these models, and find the central charge is c = - 2. We also show that the dimer model on the cylinder with an odd number of sites on the perimeter exhibits the same finite-size corrections as on the plane.

14 pages

References in corpus (6)

• "Exact" Algorithm for Random-Bond Ising Models in 2D
• Packing dimers on $(2p+1)\times (2q+1)$ lattices
• Bond-Propagation Algorithm for Thermodynamic Functions in General 2D Ising Models
• Corner contribution to percolation cluster numbers
• Accurate expansions of internal energy and specific heat of critical two-dimensional Ising model with free boundaries
• Corner contribution to cluster numbers in the Potts model

Cited by in corpus (8)

• Exact solution of the $2d$ dimer model: Corner free energy, correlation functions and combinatorics
• Integrability and conformal data of the dimer model
• Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition
• Finite-size corrections and scaling for the dimer model on the checkerboard lattice
• Exact finite-size corrections in the dimer model on a planar square lattice
• Exact finite-size corrections for the spanning-tree model under different boundary conditions
• Exact finite-size corrections in the dimer model on a cylinder
• Universality and exact finite-size corrections for spanning trees on cobweb and fan networks