Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact enumeration of the Critical States in the Oslo Model   We determine analytically the number $N_{\mathcal{R}}(L)$ of recurrent states
in the 1d Oslo model as a function of system size L. The solution
$N_{\mathcal{R}}(L) = \frac{1+\sqrt{5}}{2\sqrt{5}}(\frac{3+\sqrt{5}}{2})^L +
\frac{\sqrt{5}-1}{2\sqrt{5}}(\frac{3-\sqrt{5}}{2})^L$ is in exact agreement
with the number enumerated in computer simulations for $L = 1 - 10$. For $L \gg
1$, the number of allowed metastable states in the attractor increases
exponentially as $N_{\mathcal{R}}(L) \approx c_+ {\lambda}_+^L$, where
$\lambda_+ = \frac{3+\sqrt{5}}{2}$ is the golden mean. The system is
non-ergodic in the sense that the states in the attractor are not equally
probable.

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The categories of this paper are: comp-gas
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an