Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random matrix theory and critical phenomena in quantum spin chains   We compute critical properties of a general class of quantum spin chains
which are quadratic in the Fermi operators and can be solved exactly under
certain symmetry constraints related to the classical compact groups $U(N)$,
$O(N)$ and $Sp(2N)$. In particular we calculate critical exponents $s$, $\nu$
and $z$, corresponding to the energy gap, correlation length and dynamic
exponent respectively. We also compute the ground state correlators
$\left\langle \sigma^{x}_{i} \sigma^{x}_{i+n} \right\rangle_{g}$, $\left\langle
\sigma^{y}_{i} \sigma^{y}_{i+n} \right\rangle_{g}$ and $\left\langle
\prod^{n}_{i=1} \sigma^{z}_{i} \right\rangle_{g}$, all of which display
quasi-long-range order with a critical exponent dependent upon system
parameters. Our approach establishes universality of the exponents for the
class of systems in question.

27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys