Variational approximations for square lattice models in statistical mechanics
- 139 Downloads
This paper concerns a square lattice, Ising-type model with interactions between the four spins at the corners of each face. These may include nearest and next-nearest-neighbor interactions, and interactions with a magnetic field. Provided the Hamiltonian is symmetric with respect to both row reversal and column reversal, a rapidly convergent sequence of variational approximations is obtained, giving the free energy and other thermodynamic properties. For the usual Ising model, the lowest such approximations are those of Bethe and of Kramers and Wannier. The method provides a new definition of corner transfer matrices.
Key wordsStatistical mechanics lattice statistics Ising models variational approximation corner transfer matrices
Unable to display preview. Download preview PDF.
- 1.R. J. Baxter,J. Math. Phys. 9:650 (1968).Google Scholar
- 2.S. B. Kelland,Can. J. Phys. 54:1621 (1976).Google Scholar
- 3.S. K. Tsang, to be published.Google Scholar
- 4.R. J. Baxter,J. Stat. Phys. 15:485 (1976).Google Scholar
- 5.R. J. Baxter,J. Stat. Phys. 17:1 (1977).Google Scholar
- 6.C. Domb,Adv. Phys. 9:149 (1977).Google Scholar
- 7.H. A. Kramers and G. H. Wannier,Phys. Rev. 60:263 (1941).Google Scholar
- 8.I. G. Enting and R. J. Baxter,J. Phys. A: Math. Gen. 10:L117 (1977).Google Scholar
- 9.H. C. Bolton and D. W. R. Gruen,Phys. Rev. B 15:4544 (1977).Google Scholar
- 10.M. N. Barber and R. J. Baxter,J. Phys. C: Solid State Phys. 6:2913 (1973).Google Scholar
- 11.R. J. Baxter and S. B. Kelland,J. Phys. C: Solid State Phys. 7:L403 (1974).Google Scholar