Journal
ELECTRONIC JOURNAL OF PROBABILITY
Volume 28, Issue -, Pages -Publisher
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/23-EJP933
Keywords
spin glasses; second moment; replica symmetry
Categories
Ask authors/readers for more resources
Excluding some special cases, computing the critical inverse-temperature beta c 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 beta m <= beta c to the critical inverse-temperature. Interestingly, in the important case of the Sherrington-Kirkpatrick model beta m = beta c. 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 beta m = beta c. In particular, for those models we obtain the value of beta c.
Excluding some special cases, computing the critical inverse-temperature beta c 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 beta m <= beta c to the critical inverse-temperature. Interestingly, in the important case of the Sherrington-Kirkpatrick model beta m = beta c. 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 beta m = beta c. In particular, for those models we obtain the value of beta c.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available