The purpose of this paper is to face up the statistical mechanics of dense spin glasses using the well-known Ising case as a prelude for testing the methodologies we develop and then focusing on the Gaussian case as the main subject of our investigation. We tackle the problem of solving for the quenched statistical pressures of these models both at the replica symmetric level and under the first step of replica symmetry breaking by relying upon two techniques: the former is an adaptation of the celebrated Guerra’s interpolation (closer to probability theory in its spirit) and the latter is an adaptation of the transport partial differential equation (closer to mathematical physics in spirit). We recover, in both assumptions, the same expression for quenched statistical pressure and self-consistency equation found with other techniques, including the well-known replica trick technique.
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April 2022
Research Article|
April 05 2022
On Gaussian spin glass with P-wise interactions
Linda Albanese
;
Linda Albanese
a)
Dipartimento di Matematica e Fisica Ennio De Giorgi, Università del Salento
, Via per Arnesano, 73100 Lecce, Italy
and Scuola Superiore ISUFI, Campus Ecotekne
, Via Monteroni, 73100 Lecce, Italy
a)Author to whom correspondence should be addressed: linda.albanese@unisalento.it. Also at: Istituto Nazionale di Fisica Nucleare, Campus Ecotekne, Via Monteroni, 73100 Lecce, Italy.
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Andrea Alessandrelli
Andrea Alessandrelli
Dipartimento di Matematica e Fisica Ennio De Giorgi, Università del Salento
, Via per Arnesano, 73100 Lecce, Italy
and Scuola Superiore ISUFI, Campus Ecotekne
, Via Monteroni, 73100 Lecce, Italy
Search for other works by this author on:
a)Author to whom correspondence should be addressed: linda.albanese@unisalento.it. Also at: Istituto Nazionale di Fisica Nucleare, Campus Ecotekne, Via Monteroni, 73100 Lecce, Italy.
J. Math. Phys. 63, 043302 (2022)
Article history
Received:
November 24 2021
Accepted:
March 09 2022
Citation
Linda Albanese, Andrea Alessandrelli; On Gaussian spin glass with P-wise interactions. J. Math. Phys. 1 April 2022; 63 (4): 043302. https://doi.org/10.1063/5.0079776
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