CROSSOVER FROM EXTENSIVE TO NONEXTENSIVE BEHAVIOR DRIVEN BY LONG-RANGE INTERACTIONS

We determine, through numerical energy optimization, the fundamental-state energy E associated with an extended model for ferrofluids (colloidal suspension of magnetic particles assumed to form rings of N dipoles). The extension consists in generalizing, into 1/r (0), a standard 1/r6 contribution to the attrative potential. We show that N, N lnN, or N2-, respectively, for >1, =1, or 0<1. In addition, a connection with generalized statistical mechanics is conjecturally proposed and the analogy with the d=2 XY ferromagnet is exhibited. © 1995 The American Physical Society.