The full replica symmetry breaking in the Ising spin glass on random regular graph

Abstract

In this paper, we extend the full replica symmetry breaking scheme to the Ising spin glass on a random regular graph. We propose a new martingale approach, that overcomes the limits of the Parisi-Mézard cavity method, providing a well-defined formulation of the full replica symmetry breaking problem in random regular graphs. Finally, we define the order parameters of the system and get a set of self-consistency equations for the order parameters and the free energy. We face up the problem only from a technical point of view: the physical meaning of this approach and the quantitative evaluation of the solution of the self-consistency equations will be discussed in next works.

23 pages

References in corpus (4)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• On exchangeable random variables and the statistics of large graphs and hypergraphs
• The cavity method at zero temperature
• The marginally stable Bethe lattice spin glass revisited

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