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For a large class of repulsive interaction models, the Mayer cluster integrals can be transformed into a tridiagonal symmetric matrix, whose elements converge to a constant with a 1/n^2 correction. We find exact expressions, in terms of these correction terms, for the two critical exponents describing the density near the two singular termination points of the fluid phase. We apply the method to the hard-spheres model and find that the metastable fluid phase terminates at rho_t=0.751(5). The density near the transition is given by (rho_t-rho)~(z_t-z)^sigma', where the critical exponent is predicted to be sigma'=0.0877(25). The termination density is close to the observed glass transition, and thus the above critical behavior is expected to characterize the onset of glassy behavior in hard spheres.
Comment: Uses RevTEX and psfig.sty (included). 10 pages. Submitted to J.Phys.A
Comment: 1 file, 10 pages, LaTex, no figures
The Binder cumulant (BC) has been widely used for locating the phase transition point accurately in systems with thermal noise. In systems with quenched disorder, the BC may show subtle finite-size effects due to large sample-to-sample fluctuations. We study the globally coupled Kuramoto model of interacting limit-cycle oscillators with random natural frequencies and find an anomalous dip in the BC near the transition. We show that the dip is related to non-self-averageness of the order parameter at the transition. Alternative definitions of the BC, which do not show any anomalous behavior regardless of the existence of non-self-averageness, are proposed.
Commonly, normal diffusive behavior is characterized by a linear dependence of the second central moment on time, $< x^2(t) >\propto t$, while anomalous behavior is expected to show a different time dependence, $ < x^2(t) > \propto t^{\delta}$ with $\delta <1$ for subdiffusive and $\delta >1$ for superdiffusive motions. Here we demonstrate that this kind of qualification, if applied straightforwardly, may be misleading: There are anomalous transport motions revealing perfectly "normal" diffusive character ($< x^2(t) >\propto t$), yet being non-Markov and non-Gaussian in nature. We use recently developed framework \cite[Phys. Rev. E \textbf{75}, 056702 (2007)]{magdziarz2007b} of Monte Carlo simulations which incorporates anomalous diffusion statistics in time and space and creates trajectories of such an extended random walk. For spec...
Comment: 11 pages, new appendix with comparison to known rigorous results
Comment: 11 pages, no figures. This version is consistent with the accepted (now published) paper.
Comment: 46 pages, 3 figures. International Workshop on Econophysics, Budapest, July 21-27, 1997.
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