SPIN-SPIN CORRELATIONS I A FINITE-SIZED SPHERICAL MODEL UNDER TWISTED BOUNDARY-CONDITIONS

Finite-size effects in the correlation function G(R, T; L) of a spherical-model ferromagnet, confined to geometry L(d - d') X infinity(d') (2 < d < 4, d' less-than-or-equal-to 2) and subjected to twisted boundary conditions, are analyzed. Focusing our attention on the region of first-order phase transition (T < T(c)), we examine the influence of the twist parameter tau on the function G(R, T; L) in different regimes of the distance parameter epsilon (= R/L). We find that the functional dependence of the function G on the parameter epsilon is highly anisotropic, in that it depends very differently on the components, epsilon(perpendicular-to) and epsilon(parallel-to), of epsilon pertaining to the finite and the infinite directions, respectively. While the long-range order in the direction of epsilon(perpendicular-to) is significantly altered by the parameter tau, it is curtailed very seriously in the direction of epsilon(parallel-to). In fact, for epsilon(parallel-to) >> 1, the qualitative features of the correlation function acquire characteristics of a d'-dimensional bulk system, though the correlation length xi appearing therein still pertains to the actual, finite-sized system. The net result is that long-range order in the direction of R(parallel-to) persists only to distances small in comparison with xi which, for d' < 2, is known to be O{L(L/a)(d - 2)/(2 - d')}, a being the lattice constant.