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Exact finite-size corrections and corner free energies for the \(c = - 2\) universality class. (English) Zbl 1323.82009

Summary: We consider the partition functions of the anisotropic dimer model on the rectangular \((2 M - 1) \times(2 N - 1)\) lattice with (a) free and (b) cylindrical boundary conditions with a single monomer residing on the boundary. 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.

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82D60 Statistical mechanics of polymers
82B27 Critical phenomena in equilibrium statistical mechanics
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T25 Quantum field theory on lattices
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
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