Studies of Lattice Spin Models and Their Critical Behavior.

Akai Kurbanovich Murtazaev

Zhou Li-ling

Using the two-spin cluster mean-field approximation method,the critical behavior of the mixed-spin(s = 1,s = 1/2) Heisenberg model on the cubic lattice was studied.For diferent anisotropic values,the thermal behavior of the magnetization were obtained.The results indicate that the mixed-spin Heisenberg system presents second-order phase transition,and the anisotropic value has influence on the critical temperature.

Gareth O. Williams

A. Pawlak

The nonasymptotic critical behavior of sound attenuation coefficient has been studied in an elastically isotropic Ising system above the critical point on the basis of a complete stochastic model including both spin-energy and lattice-energy modes linearly coupled to the longitudinal sound mode. The effect of spin-lattice relaxation on the ultrasonic attenuation is investigated. The crossover between weak-singularity behavior $t^{-2 α}$ and strong singularity behavior $t^{-(z ν+α)}$ is studied. A new high-frequency regime with singularity of the type $t^{-z ν+α}$ is discovered in the magnetic systems. This new regime corresponds to an adiabatic sound propagation and is very similar to the ones in binary mixture and liquid helium. A new frequency-dependent specific-heat being the harmonic average of the bare lattice and critical spin specific-heats is introduced. It was shown that such specific-heat descibes the process of equilibrization between spin and lattice subsystems and includes the most important features of critical sound attenuation. In some regions of coupling constants the acoustic self-energy can be very well approximated solely by this quantity.

Paraj Titum, Mohammad F. Maghrebi

Denis Dalmazi, Fernanda Lopes Sá

Renormalization group arguments based on a ıφ 3 field theory lead us to expect a certain universal behavior for the density of partition function zeros in spin models with short-range interaction. Such universality has been tested analytically and numerically in different d = 1 and higher dimensional spin models. In d = 1, one finds usually the critical exponent σ = −1/2. Recently, we have shown in the d = 1 Blume–Emery–Griffiths (BEG) model on a periodic static lattice (one ring) that a new critical behavior with σ = −2/3 can arise if we have a triple degeneracy of the transfer matrix eigenvalues. Here we define the d = 1 BEG model on a dynamic lattice consisting of connected and non-connected rings (non-periodic lattice) and check numerically that also in this case we have mostly σ = −1/2 while the new value σ = −2/3 can arise under the same conditions of the static lattice (triple degeneracy) which is a strong check of universality of the new value of σ. We also show that although such conditions are necessary, they are not sufficient to guarantee the new critical behavior.