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

Abstract

We show the presence of a first-order phase transition for a ferromagnetic Ising model on ${\mathbb{Z}}^2$ 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 $L_1\times L_2$ sites, such that the total value of the external field is zero. The phase transition holds if $h<\frac{2J}{L_1}+\frac{2J}{L_2}$, 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.

24 pages, 4 figures

References in corpus (5)

• Reflection positivity and phase transitions in lattice spin models
• A selection of nonequilibrium issues
• Forbidden gap argument for phase transitions proved by means of chessboard estimates
• Phase Transitions in Ferromagnetic Ising Models with spatially dependent magnetic fields
• Phase Transition in Ferromagnetic Ising Models with Non-Uniform External Magnetic Fields

Cited by in corpus (1)

• Lack of phase transitions in staggered magnetic systems. A comparison of uniqueness criteria