Periodic minimizers in 1D local mean field theory

Alessandro Giuliani, Joel Lebowitz, Elliott H. Lieb

Research output: Contribution to journalArticle

16 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)163-177
Number of pages15
JournalCommunications In Mathematical Physics
Volume286
Issue number1
DOIs
StatePublished - Feb 1 2009

Fingerprint

Mean-field Theory
Local Field
Minimizer
Reflection Positivity
Lattice System
Long-range Interactions
Interaction
Ground State
Free Energy
Nearest Neighbor
interactions
Zero
Energy
free energy
ground state
energy
Class

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Giuliani, Alessandro ; Lebowitz, Joel ; Lieb, Elliott H. / Periodic minimizers in 1D local mean field theory. In: Communications In Mathematical Physics. 2009 ; Vol. 286, No. 1. pp. 163-177.
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Periodic minimizers in 1D local mean field theory. / Giuliani, Alessandro; Lebowitz, Joel; Lieb, Elliott H.

In: Communications In Mathematical Physics, Vol. 286, No. 1, 01.02.2009, p. 163-177.

Research output: Contribution to journalArticle

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