Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Transverse Field Spin-Glass Model on the Cayley tree : phase
  transition between the two Many-Body-Localized Phases   The quantum Ising model with random couplings and random transverse fields on
the Cayley tree is studied by Real-Space-Renormalization in order to construct
the whole set of eigenstates. The renormalization rules are analyzed via large
deviations. The phase transition between the paramagnetic and the spin-glass
Many-Body-Localized phases involves the activated exponent $\psi=1$ and the
correlation length exponent $\nu=1$. The spin-glass-ordered cluster containing
$N_{SG}$ spins is found to be extremely sparse with respect to the total number
$N$ of spins : its size grows only logarithmically at the critical point
$N_{SG}^{criti} \propto \ln N$, and it is sub-extensive $N_{SG} \propto
N^{\theta}$ in the finite region of the spin-glass phase where the continuously
varying exponent $\theta$ remains in the interval $0<\theta<1$.

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The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn