Analytical study of the antiferromagnetic Heisenberg films

With the variational cumulant expansion (VCE) method, the thermodynamic beh aviors of S = 1/2 antiferromagnetic Heisenberg films in simple cubic lattic es are studied analytically. From the analytic properties of the free energ y, in principle we are able to calculate analytically the critical temperat ures T-c(L) and the thermodynamic functions, to any order cumulant as the f unctions of the number of L (the hyperlayers in the hyperfilm). Explicit ex pressions for T-c(L) up to the fourth order are given. A comparison with th e existing results for 3-dimensional system is given. The effective range o f the interaction is obtained from numerical results.