A Phase Transition in a Quenched Amorphous Ferromagnet

作者：Daletskii Alexei; Kondratiev Yuri; Kozitsky Yuri^*; Pasurek Tanja

来源：Journal of Statistical Physics, 2014, 156(1): 156-176.

DOI：10.1007/s10955-014-0996-9

• Random Gibbs measure
• Geometric random graph
• Poisson point process
• Percolation
• Unbounded spin model
• Wells inequality

Quenched thermodynamic states of an amorphous ferromagnet are studied. The magnet is a countable collection of point particles chaotically distributed over R-d, d %26gt;= 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 intensity of the underlyin

• 出版日期2014-7