Alexei Daletskii, Yuri Kondratiev, Yuri Kozitsky, Tanja Pasurek
Quenched thermodynamic states of an amorphous ferromagnet are studied. The magnet is a countable collection of point particles chaotically distributed over R^d, d \geq 2, which is modeled by a homogeneous Poisson point process. Each particle bears a real-valued spin with symmetric a priori distribution; the spin-spin interaction is pairwise and attractive. For every pair of particles, the interaction intensity is random with distribution dependent on the Euclidean distance between the particles. The intensities are independent of the underlying Poisson point process and also of each other for distinct pairs of particles. For this model, we prove that with probability one: (a) quenched thermodynamic states exist; (b) they are multiple if the particle density and the interaction strength are large enough.
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http://arxiv.org/abs/1303.0761
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