Communications in Mathematical Physics

, Volume 286, Issue 1, pp 163–177

Periodic Minimizers in 1D Local Mean Field Theory

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

DOI: 10.1007/s00220-008-0589-z

Cite this article as:
Giuliani, A., Lebowitz, J.L. & Lieb, E.H. Commun. Math. Phys. (2009) 286: 163. doi:10.1007/s00220-008-0589-z


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.

Copyright information

© The Author(s) 2008

Authors and Affiliations

  • Alessandro Giuliani
    • 1
  • Joel L. Lebowitz
    • 2
  • Elliott H. Lieb
    • 3
  1. 1.Department of PhysicsPrinceton UniversityPrincetonUSA
  2. 2.Departments of Mathematics and PhysicsRutgers UniversityPiscatawayUSA
  3. 3.Departments of Mathematics and PhysicsPrinceton UniversityPrincetonUSA
  4. 4.Dipartimento di Matematica di Roma TreRomaItaly

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