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Cross-over phenomena in the asymptotic behaviour of lattice sums

M N Barber

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Ssigma (k, beta ), of a given form, over a d-dimensional lattice are analysed for small beta and k= mod k mod . In particular, for non-integral sigma , Ssigma (k, beta ) is shown to have a singular part and to exhibit cross-over phenomena. Explicit results for the cross-over function are obtained.


PACS

05.50.+q Lattice theory and statistics (Ising, Potts, etc.)

MSC

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

Subjects

Statistical physics and nonlinear systems

Dates

Issue 12 (December 1977)



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