Phase Transitions in Ferromagnetic Ising Models with spatially dependent magnetic fields

Abstract

In this paper we study the nearest neighbor Ising model with ferromagnetic interactions in the presence of a space dependent magnetic field which vanishes as $|x{|}^{-\alpha }$, $\alpha >0$, as $|x|\to \infty$. We prove that in dimensions $d\ge 2$ for all $\beta$ large enough if $\alpha >1$ there is a phase transition while if $\alpha <1$ there is a unique DLR state.

arXiv commentto appear in Communications in Mathematical Physics

References in corpus (4)

• Graphical Representations for Ising Systems in External Fields
• Phase Transition in the 1d Random Field ising model with long range interaction
• Phase Transition in Ferromagnetic Ising Models with Non-Uniform External Magnetic Fields
• Typical Gibbs configurations for the 1d Random Field Ising Model with long range interaction

Cited by in corpus (12)

• Graphical Representations for Ising and Potts Models in General External Fields
• Contour methods for long-range Ising models: weakening nearest-neighbor interactions and adding decaying fields
• Infinite DLR Measures and Volume-Type Phase Transitions on Countable Markov Shifts
• Phase transition in ferromagnetic Ising model with a cell-board external field
• The critical 1-arm exponent for the ferromagnetic Ising model on the Bethe lattice
• Stability of the Phase Transition of Critical-Field Ising Model on Cayley trees under Inhomogeneous External Fields
• Thermodynamic Formalism for Generalized Markov Shifts on Infinitely Many States
• Long-Range Ising Models: Contours, Phase Transitions and Decaying Fields
• Fixed-magnetization Ising model with a slowly varying magnetic field
• Multidimensional Contours à la Fröhlich-Spencer and Boundary Conditions for Quantum Spin Systems
• Sharp Phase Transition for the Random-Cluster Model with Summable External Magnetic Field
• Poisson Statistics in the Non-Homogeneous Hierarchical Anderson Model