TY - JOUR

T1 - Periodic minimizers in 1D local mean field theory

AU - Giuliani, Alessandro

AU - Lebowitz, Joel L.

AU - Lieb, Elliott H.

N1 - Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.

PY - 2009/2

Y1 - 2009/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=58149514134&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58149514134&partnerID=8YFLogxK

U2 - 10.1007/s00220-008-0589-z

DO - 10.1007/s00220-008-0589-z

M3 - Article

AN - SCOPUS:58149514134

VL - 286

SP - 163

EP - 177

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -