, Volume 286, Issue 1, pp 163-177
Date: 27 Aug 2008

Periodic Minimizers in 1D Local Mean Field Theory

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Abstract

There are not many physical systems where it is possible to demonstate rigorously that energy minimizers are periodic. Using reflection positivity techniques we prove, for a class of mesoscopic free-energies representing 1D systems with competing interactions, that all minimizers are either periodic, with zero average, or of constant sign. Examples of both phenomena are given. This extends our previous work where such results were proved for the ground states of lattice systems with ferromagnetic nearest neighbor interactions and dipolar type antiferromagnetic long range interactions.

Communicated by H. Spohn
© 2008 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.