We apply for the first time a new one-loop topological expansion around the Bethe solution to the spin-glass model with a field in the high connectivity limit, following the method- ological scheme proposed in a recent work. The results are completely equivalent to the well-known ones, found by standard field-theoretical expansion around the fully connected model (Bray and Roberts 1980, and following works). However this method has the advantage that the starting point is the original Hamiltonian of the model, with no need to define an associated field theory, nor to know the initial values of the couplings, and the computations have a clear and simple phys- ical meaning. Moreover this new method can also be applied in the case of zero temperature, when the Bethe model has a transition in field, contrary to the fully connected model that is always in the spin-glass phase. Sharing with finite-dimensional model the finite connectivity properties, the Bethe lattice is clearly a better starting point for an expansion with respect to the fully connected model. The present work is a first step towards the generalization of this new expansion to more difficult and interesting cases as the zero-temperature limit, where the expansion could lead to different results with respect to the standard one.

One-loop topological expansion for spin glasses in the large connectivity limit / Chiara Angelini, Maria; Parisi, Giorgio; Ricci-Tersenghi, Federico. - In: EUROPHYSICS LETTERS. - ISSN 0295-5075. - 121:2(2018), p. 27001. [10.1209/0295-5075/121/27001]

One-loop topological expansion for spin glasses in the large connectivity limit

Chiara Angelini, Maria;Parisi, Giorgio;Ricci-Tersenghi, Federico
2018

Abstract

We apply for the first time a new one-loop topological expansion around the Bethe solution to the spin-glass model with a field in the high connectivity limit, following the method- ological scheme proposed in a recent work. The results are completely equivalent to the well-known ones, found by standard field-theoretical expansion around the fully connected model (Bray and Roberts 1980, and following works). However this method has the advantage that the starting point is the original Hamiltonian of the model, with no need to define an associated field theory, nor to know the initial values of the couplings, and the computations have a clear and simple phys- ical meaning. Moreover this new method can also be applied in the case of zero temperature, when the Bethe model has a transition in field, contrary to the fully connected model that is always in the spin-glass phase. Sharing with finite-dimensional model the finite connectivity properties, the Bethe lattice is clearly a better starting point for an expansion with respect to the fully connected model. The present work is a first step towards the generalization of this new expansion to more difficult and interesting cases as the zero-temperature limit, where the expansion could lead to different results with respect to the standard one.
2018
Spin-glass and other random models; Renormalization group methods
01 Pubblicazione su rivista::01a Articolo in rivista
One-loop topological expansion for spin glasses in the large connectivity limit / Chiara Angelini, Maria; Parisi, Giorgio; Ricci-Tersenghi, Federico. - In: EUROPHYSICS LETTERS. - ISSN 0295-5075. - 121:2(2018), p. 27001. [10.1209/0295-5075/121/27001]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1088072
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