Correlation Function of the Two-Dimensional Ising Model on a Finite Lattice: II

We calculate the pair correlation function and the magnetic susceptibility in the anisotropic Ising model on the lattice with one infinite and one finite dimension with periodic boundary conditions imposed along the second dimension. Using the exact expressions for lattice form factors, we propose formulas for arbitrary spin matrix elements, thus providing a possibility to calculate all multipoint correlation functions in the anisotropic Ising model on cylindrical and toroidal lattices. We analyze passing to the scaling limit.

[1]  Solution of the 2D ising model on a triangular lattice by the method of auxiliaryq-deformed Grassmann fields , 1996 .

[2]  C. Tracy,et al.  Two-dimensional Ising correlations: Convergence of the scaling limit , 1981 .

[3]  Ising Field Theory in a Magnetic Field: Analytic Properties of the Free Energy , 2001, hep-th/0112167.

[4]  Finite temperature correlations in the one-dimensional quantum Ising model. , 1996, cond-mat/9606104.

[5]  O. Lisovyy for the correlation functions of the 2D Ising model on the cylinder , 2001, hep-th/0108015.

[6]  Universal, finite-temperature, crossover functions of the quantum transition in the Ising chain in a transverse field , 1995, cond-mat/9509147.

[7]  V. N. Plechko Simple solution of two-dimensional ising model on a torus in terms of Grassmann integrals , 1985 .

[8]  O. Lisovyy,et al.  Spin matrix elements in 2D Ising model on the finite lattice , 2003, 0708.3625.

[9]  On correlation functions of the XY model , 1998 .

[10]  N. Kitanine,et al.  Form factors of the XXZ Heisenberg spin-1/2 finite chain , 1998, math-ph/9807020.

[11]  A. I. Bugrii Correlation Function of the Two-Dimensional Ising Model on a Finite Lattice: I , 2001 .

[12]  B. McCoy The connection between statistical mechanics and quantum field theory , 1994, hep-th/9403084.

[13]  Alexander B. Zamolodchikov,et al.  Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models , 1979 .

[14]  A. I. Bugrij,et al.  The correlation function in two dimensional Ising model on the finite size lattice. I , 2000, hep-th/0011104.

[15]  B. Berg,et al.  Construction of Green's functions from an exact S matrix , 1979 .

[16]  F. Smirnov Form Factors in Completely Integrable Models of Quantum Field Theory , 1992 .

[17]  C. Tracy,et al.  Spin spin correlation functions for the two-dimensional Ising model: Exact theory in the scaling region , 1976 .

[18]  Keiji Yamada On the Spin-Spin Correlation Function in the Ising Square Lattice and the Zero Field Susceptibility , 1984 .

[19]  S. Lukyanov Finite Temperature Expectation Values of Local Fields in the sinh-Gordon model , 2000 .