Vector breaking of replica symmetry in some low temperature disordered systems

Abstract

We present a new method to study disordered systems in the low temperature limit. The method uses the replicated Hamiltonian. It studies the saddle points of this Hamiltonian and shows how the various saddle point contributions can be resummed in order to obtain the scaling behaviour at low temperatures. In a large class of strongly disordered systems, it is necessary to include saddle points of the Hamiltonian which break the replica symmetry in a vector sector, as opposed to the usual matrix sector breaking of spin glass mean field theory.

Latex, 26 pages, 1 postscript figure

References in corpus (3)

• Glassy transition in the three-dimensional random field Ising model
• Random field Ising model: dimensional reduction or spin-glass phase?
• Some non perturbative calculations on spin glasses

Cited by in corpus (16)

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• Symmetry relation for multifractal spectra at random critical points
• Random Bond Potts Model: the Test of the Replica Symmetry Breaking
• The Distributional Zeta-Function in Disordered Field Theory
• Griffiths singularity in the random Ising ferromagnet
• Parisi-Symmetry of the Many-Body Quantum Theory of randomly interacting fermionic systems
• Spontaneous symmetry breaking in replica field theory
• On the dynamics of Kac $p$-spin glasses
• Mesoscopic charging effects in the $\sigma$-model for granular metals
• Off-perturbative states in disordered systems
• Anomalous finite size corrections in random field models
• Finite-Size Effects in Disordered $\lambda {\varphi }^4$ Model
• Calculation of 1RSB transition temperature of spin glass models on regular random graphs under the replica symmetric ansatz