06-71 Dmitry Ioffe and Anna Levit

Long range order and giant components of quantum random graphs (308K, pdf) Mar 15, 06

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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 $\gamma_c$.

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