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

Nickolay Izmailian; Ralph Kenna; Wenan Guo; Xintian Wu

doi:10.1016/j.nuclphysb.2014.04.023

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

Nickolay Izmailian, Ralph Kenna, Wenan Guo, Xintian Wu

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Abstract

We consider the partition functions of the anisotropic dimer model on the rectangular (2. M - 1) × (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.

Original language	English
Pages (from-to)	157-171
Number of pages	15
Journal	Nuclear Physics B
Volume	884
Issue number	1
Early online date	30 Apr 2014
DOIs	https://doi.org/10.1016/j.nuclphysb.2014.04.023
Publication status	Published - 1 Jul 2014

Bibliographical note

This is an open access article under the CC-BY license

Funding

W.G. wishes to thank J.L. Jacobsen for drawing our attention to this subject. The work of W.G. and X.W. were supported by the National Natural Science Foundation of China under Grant No. 11175018 . The work of N.I. and R.K. were supported by a Marie Curie IIF (Project No. 300206 -RAVEN) and IRSES (Projects Nos. 295302 -SPIDER and 612707 -DIONICOS) within 7th European Community Framework Programme and by the grant of the Science Committee of the Ministry of Science and Education of the Republic of Armenia under contract 13-1C080 .

ASJC Scopus subject areas

Nuclear and High Energy Physics

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N2 - We consider the partition functions of the anisotropic dimer model on the rectangular (2. M - 1) × (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.

AB - We consider the partition functions of the anisotropic dimer model on the rectangular (2. M - 1) × (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.

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

Abstract

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