Site Disordered Spin Systems in the Gaussian Variational Approximation

Abstract

We 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.

Replaced with version to be published. 33 pages, 3 postscript figures, using harvmac. Also available at http://chimera.roma1.infn.it/index_papers_complex.html

References in corpus (7)

• The structural glass transition and the entropy of the metastable states
• Replica Symmetry Breaking in the Critical Behaviour of the Random Ferromagnet
• Glassy transition in the three-dimensional random field Ising model
• Replica Symmetry Breaking Instability in the 2D XY model in a random field
• Block diagonalizing ultrametric matrices
• Replica Symmetry Breaking in Renormalization: Application to the Randomly Pinned Planar Flux Array
• A Field Theory for Finite Dimensional Site Disordered Spin Systems

Cited by in corpus (1)

• Spontaneous versus explicit replica symmetry breaking in the theory of disordered systems