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We consider a class of rotationally invariant unitary random matrix ensembles where the eigenvalue density falls off as an inverse power law. Under a new scaling appropriate for such power law densities (different from the scaling required in Gaussian random matrix ensembles), we calculate exactly the two-level kernel that determines all eigenvalue correlations. We show that such ensembles belong to the class of critical ensembles.
The correlation length $xi$, a key quantity in glassy dynamics, can now be precisely measured for spin glasses both in experiments and in simulations. However, known analysis methods lead to discrepancies either for large external fields or close to
We propose a generic scaling theory for critical phenomena that includes power-law and essential singularities in finite and infinite dimensional systems. In addition, we clarify its validity by analyzing the Potts model in a simple hierarchical netw
We discuss shortest-path lengths $ell(r)$ on periodic rings of size L supplemented with an average of pL randomly located long-range links whose lengths are distributed according to $P_l sim l^{-xpn}$. Using rescaling arguments and numerical simulati
We demonstrate a method to solve a general class of random matrix ensembles numerically. The method is suitable for solving log-gas models with biorthogonal type two-body interactions and arbitrary potentials. We reproduce standard results for a vari
We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a Levy walk process, often used to