David S Dean and David Lancaster 1997 J. Phys. A: Math. Gen. 30 37 doi:10.1088/0305-4470/30/1/005
David S Dean and David Lancaster
Show affiliationsWe define a replica field theory describing finite dimensional site-disordered spin systems by introducing the notion of grand canonical disorder, where the number of spins in the system is random but quenched. A general analysis of this field theory is made using the Gaussian variational or Hartree - Fock method, and illustrated with several specific examples. Irrespective of the form of interaction between the spins this approximation predicts a spin-glass phase. We discuss the replica symmetric phase at length, explicitly identifying the correlator that diverges at the spin-glass transition. We also discuss the form of continuous replica symmetry breaking found just below the transition. Finally we show how an analysis of ferromagnetic ordering indicates a breakdown of the approximation.
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.)
82B26 Phase transitions (general)
82D30 Random media, disordered materials (including liquid crystals and spin glasses)
Issue 1 (7 January 1997)
Received 10 June 1996, in final form 29 August 1996
David S Dean and David Lancaster 1997 J. Phys. A: Math. Gen. 30 37
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