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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/r^6 contribution to the attrative potential. We show that E, N lnN, or N^2-, respectively, for >1, =1, or 01. In addition, a connection with generalized statistical mechanics is conjecturally proposed and the analogy with the d=2 XY ferromagnet is exhibited.
Jund et al. (Sat,) studied this question.
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