Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-Temperature Fidelity-Metric Approach to the Lipkin-Meshkov-Glick
  Model   The fidelity metric has recently been proposed as a useful and elegant
approach to identify and characterize both quantum and classical phase
transitions. We study this metric on the manifold of thermal states for the
Lipkin-Meshkov-Glick (LMG) model. For the isotropic LMG model, we find that the
metric reduces to a Fisher-Rao metric, reflecting an underlying classical
probability distribution. Furthermore, this metric can be expressed in terms of
derivatives of the free energy, indicating a relation to Ruppeiner geometry.
This allows us to obtain exact expressions for the (suitably rescaled) metric
in the thermodynamic limit. The phase transition of the isotropic LMG model is
signalled by a degeneracy of this (improper) metric in the paramagnetic phase.
Due to the integrability of the isotropic LMG model, ground state level
crossings occur, leading to an ill-defined fidelity metric at zero temperature.

12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex