Xs. Chen et V. Dohm, ORDER-PARAMETER DISTRIBUTION FUNCTION OF FINITE O(N) SYMMETRICAL SYSTEMS IN AN EXTERNAL-FIELD, Physica. A, 235(3-4), 1997, pp. 555-572
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.