Critical Correlations and Finite Thickness Effects in the Heisenberg Model .

Vinod Mubayi

Amra Peles, B. W. Southern

The antiferromagnetic Heisenberg model on a stacked triangular geometry with a finite number of layers is studied using Monte Carlo methods. A topological phase transition occurs at finite temperature for all film thicknesses. Our results indicate that topological excitations are important for a complete understanding of the critical properties of the model between two and three dimensions.

Michael N. Barber

The grand potential pressure of an ideal boson film which is infinite in d-1 dimensions (d > 2) but of finite thickness L in the dth dimension is analysed in the limit L -+ CX), to order L -d. Across the film (i) periodic, (ii) antiperiodic, and (iii) hard wall boundary conditions are applied. The corresponding shifts in the critical temperature Te.iL) are found to vary, for large L, as (i) L -d+2 for all d ;;:. 3, (ii) L-1, L -2lnL, and L -2 for d = 3,4, and ;;:. 5 respectively, and (iii) L -1lnL and L -1 for d = 3 and ;;:. 4. With hard wall boundary conditions, the critical temperature of a sufficiently thick film exceeds that of the bulk, while the other boundary conditions depress Te. The bulk critical region is asymptotically "rounded" on a scale set by the bulk correlation length matching the thickness L in accord with the scaling theory of finite-size effects.

P. Hasenfratz, Ferenc Niedermayer A

Eugene Stanley

Hassan Chamati, Universität Duisburg–essen Fachbereich Physik

A detailed analysis of the finite–size effects on the bulk critical behaviour of the d–dimensional mean spherical model confined to a film geometry with finite thickness L is reported. Along the finite direction different boundary conditions are applied: periodic (p), antiperiodic (a) and free surfaces with Dirichlet (D), Neumann (N) and a combination of Neumann and Dirichlet (ND) on both surfaces. A systematic method for the evaluation of the finite–size corrections to the free energy for the different types of boundary conditions is proposed. The free energy density and the equation for the spherical field are computed for arbitrary d. It is found, for 2 < d < 4, that the singular part of the free energy has the required finite–size scaling form at the bulk critical temperature only for (p) and (a). For the remaining boundary conditions the standard finite–size scaling hypothesis is not valid. At d = 3, the critical amplitude (related to the so called Casimir amplitude) is estimated. We obtain