Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-size scaling properties of random transverse-field Ising chains :
  Comparison between canonical and microcanonical ensembles for the disorder   The Random Transverse Field Ising Chain is the simplest disordered model
presenting a quantum phase transition at T=0. We compare analytically its
finite-size scaling properties in two different ensembles for the disorder (i)
the canonical ensemble, where the disorder variables are independent (ii) the
microcanonical ensemble, where there exists a global constraint on the disorder
variables. The observables under study are the surface magnetization, the
correlation of the two surface magnetizations, the gap and the end-to-end
spin-spin correlation $C(L)$ for a chain of length $L$. At criticality, each
observable decays typically as $e^{- w \sqrt{L}}$ in both ensembles, but the
probability distributions of the rescaled variable $w$ are different in the two
ensembles, in particular in their asymptotic behaviors. As a consequence, the
dependence in $L$ of averaged observables differ in the two ensembles. For
instance, the correlation $C(L)$ decays algebraically as 1/L in the canonical
ensemble, but sub-exponentially as $e^{-c L^{1/3}}$ in the microcanonical
ensemble. Off criticality, probability distributions of rescaled variables are
governed by the critical exponent $\nu=2$ in both ensembles, but the following
observables are governed by the exponent $\tilde \nu=1$ in the microcanonical
ensemble, instead of the exponent $\nu=2$ in the canonical ensemble (a) in the
disordered phase : the averaged surface magnetization, the averaged correlation
of the two surface magnetizations and the averaged end-to-end spin-spin
correlation (b) in the ordered phase : the averaged gap. In conclusion, the
measure of the rare events that dominate various averaged observables can be
very sensitive to the microcanonical constraint.

12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom