FINITE-SIZE SCALING OF O(N) MODELS WITH SINGULAR BEHAVIOR - MAGNETIZATION AND SUSCEPTIBILITY IN THE PRESENCE OF AN EXTERNAL-FIELD

The analysis of a previous study (Allen and Pathria. Can. J. Phys. 67, 952 (1989)) on finite-size effects in systems with O(n) symmetry (n greater-than-or-equal-to 2), confined to geometry L(d-d') x infinity(d') (where d and d' are continuous variables such that 2 < d' < d < 4) and subjected to periodic boundary conditions, is extended (i) to include the region of first-order phase transition (T < T(c)) as well as the region of second-order phase transition (T congruent-to T(c)) and (ii) to allow the presence of an external field H > 0. Predictions, involving both amplitudes and exponents, are made on the magnetization m and susceptibility-chi in different regimes of the variables T, H, and L. Analytical verification of the predicted results is carried out in the case of the spherical model of ferromagnetism (n = infinity), and complete agreement is found.