Exact finite-size corrections for the square lattice Ising model with Brascamp-Kunz boundary conditions

Abstract

Finite-size scaling, finite-size corrections, and boundary effects for critical systems have attracted much attention in recent years. Here we derive exact finite-size corrections for the free energy F and the specific heat C of the critical ferromagnetic Ising model on the M x 2N square lattice with Brascamp-Kunz (BK) boundary conditions [J. Math. Phys. 15, 66 (1974)] and compared such results with those under toroidal boundary conditions. In the limit N \to \infty we obtain the expansion of the free energy for infinitely long strip with BK boundary conditions. Our results are consistent with the conformal field theory prediction for the mixed boundary conditions by Cardy [Nucl. Phys. {\bf B 275}, 200 (1986)] although the definitions of boundary conditions in two cases are different in one side of the long strip.

21 pages, 1 table, 2 figures

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• Kronecker's Double Series and Exact Asymptotic Expansion for Free Models of Statistical Mechanics on Torus
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• Geometric effects on critical behaviours of the Ising model
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• Universal Finite-size Scaling Functions with Exact Non-universal Metric Factors
• Exact partition functions of the Ising model on MxN planar lattices with periodic-aperiodic boundary conditions
• Shape dependent finite-size effect of critical two-dimensional Ising model on a triangular lattice
• Boundary conditions and amplitude ratios for finite-size corrections of a one-dimensional quantum spin model
• Ising model with mixed boundary conditions: universal amplitude ratios
• Simplified Transfer Matrix Approach in the Two-Dimensional Ising Model with Various Boundary Conditions
• The dimer model on the triangular lattice
• Anisotropic scaling of the two-dimensional Ising model I: the torus
• Accurate expansions of internal energy and specific heat of critical two-dimensional Ising model with free boundaries
• Exact finite-size corrections in the dimer model on a planar square lattice
• Efficient algortihms for the two dimensional Ising model with a surface field
• Mapping functions and critical behavior of percolation on rectangular domains
• Exact finite-size corrections for the spanning-tree model under different boundary conditions
• Anisotropic scaling of the two-dimensional Ising model II: surfaces and boundary fields
• The Ising model on a cylinder: universal finite size corrections and diagonalized action
• Exact coefficients of finite-size corrections in the Ising model with Brascamp-Kunz boundary conditions and their relationships for strip and cylindrical geometries
• Exact finite-size corrections in the dimer model on a cylinder
• The boundary disorder correlation for the Ising model on a cylinder
• The free energy of the non-isotropic Ising lattice with Brascamp-Kunz boundary conditions