ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract The thermodynamic limit is taken using a sequence of regions all the same shape as a given region ω of volume |ω|, with a specified distribution of normal field component on ∂ω. We show that with magnetostatic interactions the limiting free energy density is bounded above by jhen where $$\bar f$$ (ϱ,B) is the free energy density for a system of density ϱ in a uniform external fieldB and the “inf” is taken over all divergence-free fieldsB with given normal component on ∂ω and all densities ϱ(x) compatible with particle number constraints of the form $$\int\limits_{\Gamma _i } {\varrho (x)d^3 x = \left| {\Gamma _i } \right|\varrho _i } $$ where Γi is a sub-region of ω. A physical argument suggests that this upper bound is the true thermodynamic limit, and that it takes account demagnetization effects. Electrostatic interactions can be treated similarly.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01609997
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