Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Permutation glass   The field of disordered systems provides many simple models in which the
competing influences of thermal and non-thermal disorder lead to new phases and
non-trivial thermal behavior of order parameters. In this paper, we add a model
to the subject by considering a system where the state space consists of
various orderings of a list. As in spin glasses, the disorder of such
"permutation glasses" arises from a parameter in the Hamiltonian being drawn
from a distribution of possible values, thus allowing nominally "incorrect
orderings" to have lower energies than "correct orderings" in the space of
permutations. We analyze a Gaussian, uniform, and symmetric Bernoulli
distribution of energy costs, and, by employing Jensen's inequality, derive a
general condition requiring the permutation glass to always transition to the
correctly ordered state at a temperature lower than that of the non-disordered
system, provided that this correctly ordered state is accessible. We in turn
find that in order for the correctly ordered state to be accessible, the
probability that an incorrectly-ordered component is energetically favored must
be less than the inverse of the number of components in the system. We show
that all of these results are consistent with a replica symmetric ansatz of the
system and argue that there is no permutation glass phase characterized by
replica symmetry breaking, but there is glassy behavior represented by a
residual entropy at zero temperature. We conclude by discussing an apparent
duality between permutation glasses and fermion gases.

24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an