Phase Transition in Ferromagnetic Ising Model with a Cell-Board External Field

We show the presence of a first-order phase transition for a ferromagnetic Ising model on Z 2 with a periodical external magnetic field. The external field takes two values h and - h , where h > 0 . The sites associated with positive and negative values of external field form a cell-board configu...

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Bibliographic Details
Published in:Journal of statistical physics 2016-01, Vol.162 (1), p.139-161
Main Authors: González-Navarrete, Manuel, Pechersky, Eugene, Yambartsev, Anatoly
Format: Article
Language:English
Subjects:
Analysis
Ferromagnetism
Magnetic fields
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Summary:We show the presence of a first-order phase transition for a ferromagnetic Ising model on Z 2 with a periodical external magnetic field. The external field takes two values h and - h , where h > 0 . The sites associated with positive and negative values of external field form a cell-board configuration with rectangular cells of sides L 1 × L 2 sites, such that the total value of the external field is zero. The phase transition holds if h < 2 J L 1 + 2 J L 2 , where J is an interaction constant. We prove the first-order phase transition using the reflection positivity method. We apply a key inequality which is usually referred to as the chessboard estimate.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-015-1392-9