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arXiv · 1712.00367

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

Francesco Concetti
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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-M\'ezard 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.

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Francesco Concetti. 2017-12-01. The full replica symmetry breaking in the Ising spin glass on random regular graph. https://doi.org/10.1007/s10955-018-2142-6

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