Geodesic
Spin-one $p$-spin glass: Exact solution for large $p$
Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 2, pp. 295-303

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We study the low-temperature properties of the $p$-spin spin glass model in the spin-one (three-state) case for large values of $p$. We show that the one-step replica symmetry-breaking phase is unstable at a very low temperature, and we calculate the explicit boundary of the stability interval, the Gardner temperature, analytically for large values of $p$. This temperature for the spin-one model has the same form of $p$-dependence as in the case of Ising spins (two states). In the one-step replica symmetry-breaking state, a quadrupolar orientational glass coexists with the spin glass and also with a regular quadrupole ordering.
Keywords: spin glass, replica approach, Gardner transition.
Mots-clés : quadrupole glass 
@article{TMF_2018_194_2_a4,
     author = {E. E. Tareeva and T. I. Schelkacheva},
     title = {Spin-one $p$-spin glass: {Exact} solution for large $p$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {295--303},
     publisher = {mathdoc},
     volume = {194},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_194_2_a4/}
}
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E. E. Tareeva; T. I. Schelkacheva. Spin-one $p$-spin glass: Exact solution for large $p$. Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 2, pp. 295-303. http://geodesic.mathdoc.fr/item/TMF_2018_194_2_a4/