### 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 language | English (US) |
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Pages (from-to) | 163-177 |

Number of pages | 15 |

Journal | Communications In Mathematical Physics |

Volume | 286 |

Issue number | 1 |

DOIs | |

State | Published - Feb 1 2009 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications In Mathematical Physics*,

*286*(1), 163-177. https://doi.org/10.1007/s00220-008-0589-z

}

*Communications In Mathematical Physics*, vol. 286, no. 1, pp. 163-177. https://doi.org/10.1007/s00220-008-0589-z

**Periodic minimizers in 1D local mean field theory.** / Giuliani, Alessandro; Lebowitz, Joel; Lieb, Elliott H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Periodic minimizers in 1D local mean field theory

AU - Giuliani, Alessandro

AU - Lebowitz, Joel

AU - Lieb, Elliott H.

PY - 2009/2/1

Y1 - 2009/2/1

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 - https://doi.org/10.1007/s00220-008-0589-z

DO - https://doi.org/10.1007/s00220-008-0589-z

M3 - Article

VL - 286

SP - 163

EP - 177

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -