Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean-Field Spin Glass models from the Cavity--ROSt Perspective   The Sherrington-Kirkpatrick spin glass model has been studied as a source of
insight into the statistical mechanics of systems with highly diversified
collections of competing low energy states. The goal of this summary is to
present some of the ideas which have emerged in the mathematical study of its
free energy. In particular, we highlight the perspective of the cavity
dynamics, and the related variational principle. These are expressed in terms
of Random Overlap Structures (ROSt), which are used to describe the possible
states of the reservoir in the cavity step. The Parisi solution is presented as
reflecting the ansatz that it suffices to restrict the variation to hierarchal
structures which are discussed here in some detail. While the Parisi solution
was proven to be correct, through recent works of F. Guerra and M. Talagrand,
the reasons for the effectiveness of the Parisi ansatz still remain to be
elucidated. We question whether this could be related to the quasi-stationarity
of the special subclass of ROSts given by Ruelle's hierarchal `random
probability cascades' (also known as GREM).

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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
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The categories of this paper are: cs