Periodic minimizers in 1D local mean field theory
Mathematical Physics
2011-09-09 v1 Statistical Mechanics
math.MP
Abstract
Using reflection positivity techniques we prove the existence of minimizers for a class of mesoscopic free-energies representing 1D systems with competing interactions. All minimizers are either periodic, with zero average, or of constant sign. If the local term in the free energy satisfies a convexity condition, then all minimizers are either periodic or constant. 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.
Cite
@article{arxiv.0712.2330,
title = {Periodic minimizers in 1D local mean field theory},
author = {Alessandro Giuliani and Joel L. Lebowitz and Elliott H. Lieb},
journal= {arXiv preprint arXiv:0712.2330},
year = {2011}
}
Comments
20 pages, 2 figures