Locating analytically critical temperature in some statistical systems

Abstract

We have found a simple criterion which allows for the straightforward determination of the order-disorder critical temperatures. The method reproduces exactly results known for the two dimensional Ising, Potts and $Z(N<5)$ models. It also works for the Ising model on the triangular lattice. For systems which are not selfdual our proposition remains an unproven conjecture. It predicts ${\beta }_c=\mathrm{0.2656...}$ for the two coupled layers of Ising spins. Critical temperature of the three dimensional Ising model is related to the free energy of the two layer Ising system.

13 pages, LATEX, TPJU-23/93 November 1993

References in corpus (2)

• Low temperature expansion for the 3-d Ising Model
• High Precision Verification of the Kosterlitz Thouless Scenario

Cited by in corpus (8)

• Exact phase diagrams for an Ising model on a two-layer Bethe lattice
• Critical exponents of the two-layer Ising model
• Critical temperatures of the three- and four-state Potts models on the kagome lattice
• Improved Transfer-Matrix Schemes of Phenomenological Renormalization
• Improved Phenomenological Renormalization Schemes
• Double Potts chain and exact results for some two-dimensional models
• Extension of a new method for locating critical temperatures
• Internal energy density of the critical three-state Potts model on the kagome lattice