Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free energy barriers in the Sherrington-Kirkpatrick model   The free energy landscape of the Sherrington-Kirkpatrik (SK) Ising spin glass
is simple in the framework of the Thouless-Anderson-Palmer (TAP) equations as
each solution (which are minima of the free energy) has associated with it a
nearby index-one saddle point. The free energy barrier to escape the minimum is
just the difference between the saddle point free energy and that at its
associated minimum. This difference is calculated for the states with free
energies $f > f_c$. It is very small for these states, decreasing as $1/N^2$,
where $N$ is the number of spins in the system. These states are not marginally
stable. We argue that such small barriers are why numerical studies never find
these states when $N$ is large. Instead the states which are found are those
which have marginal stability. For them the barriers are at least of $O(1)$.
$f_c$ is the free energy per spin below which the states develop broken
replica-symmetry like overlaps with each other. In the regime $f < f_c$ we can
only offer some possibilities based around scaling arguments. One of these
suggest that the barriers might become as large as $N^{1/3}$. That might be
consistent with recent numerical studies on the Viana-Bray model, which were at
variance with the expectations of Cugliandolo and Kurchan for the SK model.

37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex