Critical behavior of weakly-disordered anisotropic systems in two dimensions

L.S. Lima, Antonio S. T. Pires, B. V. Costa

Giancarlo Jug, B. N. Shalaev

The critical behavior of two-dimensional (2D) anisotropic systems with weak quenched disorder described by the so-called generalized Ashkin-Teller model (GATM) is studied. In the critical region this model is shown to be described by a multifermion field theory similar to the Gross-Neveu model with a few independent quartic coupling constants. Renormalization group calculations are used to obtain the temperature dependence near the critical point of some thermodynamic quantities and the large-distance behavior of the two-spin correlation function. The equation of state at criticality is also obtained in this framework. We find that random models described by the GATM belong to the same universality class as that of the two-dimensional Ising model. The critical exponent \ensuremath{\nu} of the correlation length for the three- and four-state random-bond Potts models is also calculated in a three-loop approximation. We show that this exponent is given by an apparently convergent series in \ensuremath{\epsilon}=c-1/2 (with c the central charge of the Potts model) and that the numerical values of \ensuremath{\nu} are very close to that of the 2D Ising model. This work therefore supports the conjecture (valid only approximately for the three- and four-state Potts models) of a superuniversality for the 2D disordered models with discrete symmetries. \textcopyright{} 1996 The American Physical Society.

L. De Cesare, Maria Teresa Mercaldo

Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov, V.V. Khitrintseva

The results of a Monte Carlo study of weakly structural disorder influence onnonequilibrium critical behavior of three-dimensional anisotropic Heisenberg models with spin concentration p = 0.9 are presented with its evolution from high temperature initial state. It is shown that presence of even weakly disorder changes characteristics of nonequilibrium critical behavior of anisotropic model with easy axis anisotropy type in comparison with both pure anisotropic and isotropic Heisenberg models.

佳史 守田

Shanthanu Bhardwaj