Giuliani, Alessandro and Seiringer, Robert
(2016)
*Periodic striped ground states in Ising models with competing interactions.*
Communications in Mathematical Physics, 347 (3).
pp. 983-1007.
ISSN 1432-0916

Text
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## Abstract

We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent p of the long range interaction is larger than dÂ +Â 1, with d the space dimension, this happens for all values of J smaller than a critical value Jc(p), beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for pÂ >Â 2d and J in a left neighborhood of Jc(p). In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes (dÂ =Â 2) or slabs (dÂ =Â 3), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity.

Item Type: | Article |
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DOI: | 10.1007/s00220-016-2665-0 |

Subjects: | 500 Science > 510 Mathematics 500 Science > 530 Physics |

Research Group: | Seiringer Group |

SWORD Depositor: | Sword Import User |

Depositing User: | Sword Import User |

Date Deposited: | 05 Dec 2016 14:38 |

Last Modified: | 04 Sep 2017 14:54 |

URI: | https://repository.ist.ac.at/id/eprint/688 |

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