Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nontrivial maturation metastate-average state in a one-dimensional
  long-range Ising spin glass: above and below the upper critical range   Understanding the low-temperature pure state structure of spin glasses
remains an open problem in the field of statistical mechanics of disordered
systems. Here we study Monte Carlo dynamics, performing simulations of the
growth of correlations following a quench from infinite temperature to a
temperature well below the spin-glass transition temperature $T_c$ for a
one-dimensional Ising spin glass model with diluted long-range interactions. In
this model, the probability $P_{ij}$ that an edge $\{i,j\}$ has nonvanishing
interaction falls as a power-law with chord distance,
$P_{ij}\propto1/R_{ij}^{2\sigma}$, and we study a range of values of $\sigma$
with $1/2<\sigma<1$. We consider a correlation function $C_{4}(r,t)$. A dynamic
correlation length that shows power-law growth with time $\xi(t)\propto
t^{1/z}$ can be identified in the data and, for large time $t$, $C_{4}(r,t)$
decays as a power law $r^{-\alpha_d}$ with distance $r$ when $r\ll \xi(t)$. The
calculation can be interpreted in terms of the maturation metastate averaged
Gibbs state, or MMAS, and the decay exponent $\alpha_d$ differentiates between
a trivial MMAS ($\alpha_d=0$), as expected in the droplet picture of spin
glasses, and a nontrivial MMAS ($\alpha_d\ne 0$), as in the
replica-symmetry-breaking (RSB) or chaotic pairs pictures. We find nonzero
$\alpha_d$ even in the regime $\sigma >2/3$ which corresponds to short-range
systems below six dimensions. For $\sigma < 2/3$, the decay exponent $\alpha_d$
follows the RSB prediction for the decay exponent $\alpha_s = 3 - 4 \sigma$ of
the static metastate, consistent with a conjectured statics-dynamics relation,
while it approaches $\alpha_d=1-\sigma$ in the regime $2/3<\sigma<1$; however,
it deviates from both lines in the vicinity of $\sigma=2/3$.

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The categories of this paper are: atom-ph
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
18
The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg