Structure of 1-RSB Asymptotic Gibbs Measures in the Diluted p-Spin Models
In this paper we study asymptotic Gibbs measures in the diluted p -spin models in the so called 1 -RSB case, when the overlap takes two values q ∗ , q ∗ ∈ [ 0 , 1 ] . When the external field is not present and the overlap is not equal to zero, we prove that such asymptotic Gibbs measures are describ...
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Published in | Journal of statistical physics Vol. 155; no. 1; pp. 1 - 22 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Boston
Springer US
2014
Springer |
Subjects | |
Online Access | Get full text |
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Summary: | In this paper we study asymptotic Gibbs measures in the diluted
p
-spin models in the so called
1
-RSB case, when the overlap takes two values
q
∗
,
q
∗
∈
[
0
,
1
]
.
When the external field is not present and the overlap is not equal to zero, we prove that such asymptotic Gibbs measures are described by the Mézard–Parisi ansatz conjectured in Mézard and Parisi (Eur Phys J B 20(2):217–233
2001
). When the external field is present, we prove that the overlap can not be equal to zero and all
1
-RSB asymptotic Gibbs measures are described by the Mézard–Parisi ansatz. Finally, we give a characterization of the exceptional case when there is no external field and the smallest overlap value
q
∗
=
0
, although it does not go as far as the Mézard–Parisi ansatz. Our approach is based on the cavity computations combined with the hierarchical exchangeability of pure states. |
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ISSN: | 0022-4715 1572-9613 |
DOI: | 10.1007/s10955-014-0955-5 |