Periodic minimizers in 1D local mean field theory

Alessandro Giuliani, Joel L. Lebowitz, Elliott H. Lieb

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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
Issue number1
StatePublished - Feb 2009

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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