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

Author(s)

Gonzalez-Navarrete, Manuel ^[1] ; Pechersky, Eugene ^[2] ; Yambartsev, Anatoly ^[1]

Affiliation

^[1] Univ Sao Paulo, Inst Math & Stat, Dept Stat, BR-05508090 Sao Paulo - Brazil

^[2] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow - Russia

• Document type: Journal article
• Source: Journal of Statistical Physics; v. 162, n. 1, p. 139-161, JAN 2016.
• Web of Science Citations: 0

Abstract

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 x L-2 sites, such that the total value of the external field is zero. The phase transition holds if h < 2J/L-1 + 2J/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. (AU)

• FAPESP's process: 09/52379-8 - Stochastic modeling of interacting systems
• Grantee: Fabio Prates Machado
• Support Opportunities: Research Projects - Thematic Grants