Dynamical Critical Exponent of Ising Systems: An Extension of Thompson's Approach

Julia Mihailowa Wesselinowa, Angel Todorov Apostolov

P.R. Silva, Valery B. Kokshenev

We discuss order-disorder phase transitions of classical and quantum Ising models on the basis of the Ginzburg-Landau-Wilson free-energy action and a modification of a scaling method proposed by Thompson. The two-time critical relaxation scenario, driven by thermal and quantum fluctuations, respectively, is given in terms of the slow-down critical exponent of the order-parameter excitations.

Yurij V. Holovatch

R. Matz, D. L. Hunter, Naeem Jan

P. R. Silva

Abstract An extension of a heuristic treatment of the critical behavior of the Ising model (N = 1) developed by Thompson, to the general N‐vector model is made. Two approximations for the correlation length critical exponent v as a function of the lattice spatial dimension d and of the number of components of the order parameter N are obtained. Using the hyperscaling relation, the specific heat critical exponent α is also evaluated. Finally, diagrams are constructed displaying in the plane (d, N) various regions, namely: classical critical indexes, non‐classical critical indexes, and no‐phase transition regions or regions where the critical temperature goes to zero. These diagrams are also used to separate regions with divergent specific heat (α > 0) from the ones where it has a cusp‐like behavior (α < 0).

P. R. Silva

Abstract Upper and lower bounds are estimated of the two‐point correlation function exponent, η, of the Ising model, as a function of the lattice dimensionality, d. The average value of these two bounds together with the correlation length critical exponent v(d) evaluated by Thompson, lead to a set of critical indexes which satisfy the hyperscaling relation. This set of exponents also shows an adequate agreement with the results obtained by Le‐Guillou and Zinn‐Justin for the Ising model in non‐integer dimensions, in a large range of the parameter d.