Critical properties of high-spin Ising models on anisotropic lattices
- Russian Academy of Sciences, Institute of Problems of Chemical Physics (Russian Federation), E-mail: yur@itp.ac.ru
The coordinates of the critical points of spin-S Ising models with coupling constants J and J' are calculated for 1/2 {<=} S {<=} 13/2. The calculations are performed for several values of S and {delta} {identical_to} J'/J independently by using the phenomenological renormalization-group method or (approximate) self-duality. Numerical results combined with a mean-field analysis show that the critical coupling strength for {delta} {approx} 1 (weakly anisotropic lattice) is K{sub c}{sup (S)} ({delta}) = K{sub c}{sup (S)} (1)[1 + a(1 - {delta})], where a = (d - 1)/d is independent of S (d is the space dimension). Both free energy and internal energy are determined at the critical points. An extremum of the critical internal energy is found at {delta}* element of (0, 1). The parameter {delta}* can be used as a criterion that separates quasi-isotropic and quasi-one-dimensional regimes ({delta}* < {delta} {<=} 1 and {delta} < {delta}*, respectively). The finite-size scaling amplitudes A{sub s} and A{sub e} of the inverse spin-spin and energy-energy correlation lengths are estimated. Calculations show that the amplitudes A{sub s} and A{sub e} are independent of S within the accuracy of the adopted approximations. Moreover, their ratio A{sub e}/A{sub s} is independent of the anisotropy parameter {delta}. These results support the Ising universality hypothesis.
- OSTI ID:
- 21067595
- Journal Information:
- Journal of Experimental and Theoretical Physics, Vol. 103, Issue 5; Other Information: DOI: 10.1134/S1063776106110185; Copyright (c) 2006 Nauka/Interperiodica; Article Copyright (c) 2006 Pleiades Publishing, Inc; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7761
- Country of Publication:
- United States
- Language:
- English
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