Xs. Chen et V. Dohm, RENORMALIZATION-GROUP THEORY OF CRITICAL PHENOMENA IN CONFINED SYSTEMS - ORDER-PARAMETER DISTRIBUTION FUNCTION, International journal of modern physics b, 12(12-13), 1998, pp. 1277-1290
We present a renormalization-group study of the order-parameter distri
bution function near the critical point of O(n) symmetric three-dimens
ional (3D) systems in a finite geometry. The distribution function is
calculated within the psi(4) field theory for a 3D cube with periodic
boundary conditions by means of a novel approach that appropriately de
als with the Goldstone modes below T-c. Results are given for both van
ishing and finite external field h. The results describe finite-size e
ffects near the critical point in the h-T-plane including the first-or
der transition at the coexistence line at h = 0 below T-c. Quantitativ
e theoretical predictions of the finite-size scaling function are pres
ented for the Ising (n = 1), XY (n = 2) and Heisenberg (n = 3) models.
Good agreement is found with recent Monte Carlo data.