A Phase Transition in a Quenched Amorphous Ferromagnet

Abstract

Quenched thermodynamic states of an amorphous ferromagnet are studied. The magnet is a countable collection of point particles chaotically distributed over ${\mathbb{R}}^d$, $d\ge 2$. Each particle bears a real-valued spin with symmetric a priori distribution; the spin-spin interaction is pair-wise and attractive. Two spins are supposed to interact if they are neighbors in the graph defined by a homogeneous Poisson point process. For this model, we prove that with probability one: (a) quenched thermodynamic states exist; (b) they are multiple if the particle density (i.e., the intensity of the underlying point process) and the inverse temperature are big enough; (c) there exist multiple quenched thermodynamic states which depend on the realizations of the underlying point process in a measurable way.

References in corpus (4)

• Transition from the annealed to the quenched asymptotics for a random walk on random obstacles
• N/V-limit for Langevin dynamics in continuum
• Phase Transitions and Quantum Stabilization in Quantum Anharmonic Crystals
• Phase transitions and quantum effects in anharmonic crystals

Cited by in corpus (1)

• Gibbs States on Random Configurations