TY - JOUR
T1 - On the second moment method and RS phase of multi-species spherical spin glasses
AU - Subag, Eliran
N1 - Publisher Copyright: © 2023, Institute of Mathematical Statistics. All rights reserved.
PY - 2023
Y1 - 2023
N2 - Excluding some special cases, computing the critical inverse-temperature βc of a mixed p-spin spin glass model is a difficult task. The only known method to calculate its value for a general model requires the full power of the Parisi formula. On the other hand, an easy application of the second moment method to the partition function yields an explicit lower bound βm ≤ βc to the critical inverse-temperature. Interestingly, in the important case of the Sherrington-Kirkpatrick model βm = βc. In this work we consider the multi-species spherical mixed p-spin models without external field, and characterize by a simple condition the models for which the second moment method works in the whole replica symmetric phase, namely, models such that βm = βc. In particular, for those models we obtain the value of βc.
AB - Excluding some special cases, computing the critical inverse-temperature βc of a mixed p-spin spin glass model is a difficult task. The only known method to calculate its value for a general model requires the full power of the Parisi formula. On the other hand, an easy application of the second moment method to the partition function yields an explicit lower bound βm ≤ βc to the critical inverse-temperature. Interestingly, in the important case of the Sherrington-Kirkpatrick model βm = βc. In this work we consider the multi-species spherical mixed p-spin models without external field, and characterize by a simple condition the models for which the second moment method works in the whole replica symmetric phase, namely, models such that βm = βc. In particular, for those models we obtain the value of βc.
UR - http://www.scopus.com/inward/record.url?scp=85153856054&partnerID=8YFLogxK
U2 - https://doi.org/10.1214/23-EJP933
DO - https://doi.org/10.1214/23-EJP933
M3 - مقالة
SN - 1083-6489
VL - 28
JO - Electronic Journal of Probability
JF - Electronic Journal of Probability
M1 - 50
ER -