Exact partition functions of the Ising model on M × N planar lattices with periodic–aperiodic boundary conditions
نویسنده
چکیده
Abstract. The Grassmann path integral approach is used to calculate exact partition functions of the Ising model onM×N square (sq), plane triangular (pt) and honeycomb (hc) lattices with periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodicperiodic (ap) and antiperiodic-antiperiodic (aa) boundary conditions. The partition functions are used to calculate and plot the specific heat, C/kB, as a function of the temperature, θ = kBT/J . We find that for the N × N sq lattice, C/kB for pa and ap boundary conditions are different from those for aa boundary conditions, but for the N ×N pt and hc lattices, C/kB for ap, pa, and aa boundary conditions have the same values. Our exact partition functions might also be useful for understanding the effects of lattice structures and boundary conditions on critical finite-size corrections of the Ising model.
منابع مشابه
Recursion relations for the partition function of the two - dimensional Ising model
The partition function of the two-dimensional Ising model on a square lattice with nearest-neighbour interactions and periodic boundary conditions is investigated. Kaufman [Phys. Rev. 76, 1232–1243 (1949)] gave a solution for this function consisting of four summands. The summands are rewritten as functions of a low-temperature expansion variable, resulting in polynomials with integer coefficie...
متن کاملUniversal finite-size scaling functions for critical systems with tilted boundary conditions
We calculate finite-size scaling functions ~FSSF’s! of Binder parameter g and magnetization distribution function p(m) for the Ising model on L13L2 square lattices with periodic boundary conditions in the horizontal L1 direction and tilted boundary conditions in the vertical L2 direction such that the ith site in the first row is connected with the mod(i1cL1 ,L1)th site in the L2 row of the lat...
متن کاملq-State Potts Model on Ladder Graphs
We present exact calculations of the partition function for the q-state Potts model for general q, temperature and magnetic field on strips of the square lattices of width Ly = 2 and arbitrary length Lx = m with periodic longitudinal boundary conditions. A new representation of the transfer matrix for the q-state Potts model is introduced which can be used to calculate the determinant of the tr...
متن کاملCorrelation function of the two-dimensional Ising model on a finite lattice. II
We calculate the two-point correlation function and magnetic susceptibility in the anisotropic 2D Ising model on a lattice with one infinite and the other finite dimension, along which periodic boundary conditions are imposed. Using exact expressions for a part of lattice form factors, we propose the formulas for arbitrary spin matrix elements, thus providing a possibility to compute all multip...
متن کاملDuality of the 2D Nonhomogeneous Ising Model on the Torus
Duality relations for the 2D nonhomogeneous Ising model on the finite square lattice wrapped on the torus are obtained. The partition function of the model on the dual lattice with arbitrary combinations of the periodical and antiperiodical boundary conditions along the cycles of the torus is expressed through some specific combination of the partition functions of the model on the original lat...
متن کامل