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.