Phase transition in ferromagnetic Ising model with a cell-board external field

الأصل · EN

We show the presence of a first-order phase transition for a ferromagnetic Ising model on Z² 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 L₁× L₂ sites, such that the total value of the external field is zero. The phase transition holds if h<2J/L₁+ 2J/L₂, where J is an interaction constant. We prove a first-order phase transition using the reflection positivity (RP) method. We apply a key inequality which is usually referred to as the chessboard estimate.