ORDER-PARAMETER DISTRIBUTION FUNCTION OF FINITE O(N) SYMMETRICAL SYSTEMS IN AN EXTERNAL-FIELD

We study the effect of an external field h on the order-parameter dist ribution function near the critical point of O(n) symmetric three-dime nsional (3D) systems in a finite geometry. The distribution function i s calculated within the phi(4) field theory for a 3D cube with periodi c boundary conditions by means of a new approach that appropriately de als with the Goldstone modes below T-c. The result describes finite-si ze effects near the critical point in the h-T plane including the firs t-order transition at the coexistence line at h = 0 below T-c. Theoret ical predictions of the finite-size scaling function are presented for the Ising (n = 1) and XY (n = 2) models. Good agreement is found with recent Monte Carlo data for the distribution function of the magnetiz ation of the 3D Ising model at finite h above and below T-c.