An upper bound on the free energy for classical systems with Coulomb interactions in a varying external field |
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Authors: | E R Smith O Penrose |
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Institution: | (1) Mathematics Department, University of Newcastle, New South Wales, Australia;(2) Mathematics Department, The Open University, Milton Keynes, England |
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Abstract: | The thermodynamic limit is taken using a sequence of regions all the same shape as a given region of volume ||, with a specified distribution of normal field component on . We show that with magnetostatic interactions the limiting free energy density is bounded above by jhen where
(,B) is the free energy density for a system of density in a uniform external fieldB and the inf is taken over all divergence-free fieldsB with given normal component on and all densities (x) compatible with particle number constraints of the form
where i is a sub-region of . 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. |
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