Dmitry Ioffe and Anna Levit
Long range order and giant components of quantum random graphs
(308K, pdf)

ABSTRACT.  Mean field quantum random graphs give a natural generalization of 
classical Erd\H{o}s-R\'{e}nyi percolation model on complete graph 
 $G_N$ with $p =\beta /N$. Quantum case incorporates an additional 
 parameter $\lambda\geq 0$, and the short-long range order transition 
should be studied in the $(\beta ,\lambda)$-quarter plane. In this 
work we explicitly compute the corresponding critical curve 
$\gamma_c$, and derive results on two-point functions and sizes 
of connected components in both short and long range order 
regions. In this way the classical case corresponds to the 
limiting point $(\beta_c ,0) = (1,0)$ on $\gamma_c$.