 0671 Dmitry Ioffe and Anna Levit
 Long range order and giant components of quantum random graphs
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Mar 15, 06

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Abstract. Mean field quantum random graphs give a natural generalization of
classical Erd\H{o}sR\'{e}nyi percolation model on complete graph
$G_N$ with $p =\beta /N$. Quantum case incorporates an additional
parameter $\lambda\geq 0$, and the shortlong 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 twopoint 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 $\gamma_c$.
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