2007

Network of inherent structures in spin glasses: scaling and scale-free distributions

Z. Burda 1, A. Krzywicki 2, O. C. Martin 3 Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 76 (2007) 051107 The local minima (inherent structures) of a system and their associated transition links give rise to a network. Here we consider the topological and distance properties of such a network in the context of spin glasses. We use steepest

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Mosaic length and finite interaction-range effects in a one dimensional random energy model

Silvio Franz 1, Giorgio Parisi 2, 3, 4, Federico Ricci-Tersenghi 2 Journal of Physics A: Mathematical and General 41 (2007) 324011 In this paper we study finite interaction range corrections to the mosaic picture of the glass transition as emerges from the study of the Kac limit of large interaction range for disordered models. To this aim we consider point to set correlation

Mosaic length and finite interaction-range effects in a one dimensional random energy model Lire la suite »

Many-body effects in the mesoscopic x-ray edge problem

Martina Hentschel 1, Georg Roeder 1, Denis Ullmo 2 Progress of Theoretical Physics Supplement 166 (2007) 143-151 Many-body phenomena, a key interest in the investigation of bulk solid state systems, are studied here in the context of the x-ray edge problem for mesoscopic systems. We investigate the many-body effects associated with the sudden perturbation following the x-ray excitation of a core

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Magnetic exponents of two-dimensional Ising spin glasses

F. Liers 1, O. C. Martin 2 Physical Review B 76 (2007) 060405 The magnetic critical properties of two-dimensional Ising spin glasses are controversial. Using exact ground state determination, we extract the properties of clusters flipped when increasing continuously a uniform field. We show that these clusters have many holes but otherwise have statistical properties similar to those of

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Loop model with mixed boundary conditions, qKZ equation and alternating sign matrices

Paul Zinn-Justin 1 Journal of Statistical Mechanics: Theory and Experiment (2007) P01007 The integrable loop model with mixed boundary conditions based on the 1-boundary extended Temperley–Lieb algebra with loop weight 1 is considered. The corresponding qKZ equation is introduced and its minimal degree solution described. As a result, the sum of the properly normalized components of the

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Longest increasing subsequence as expectation of a simple nonlinear stochastic PDE with a low noise intensity

E. Katzav 1, S. Nechaev 2, O. Vasilyev 3, 4 Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 75 (2007) 061113 We report some new observation concerning the statistics of Longest Increasing Subsequences (LIS). We show that the expectation of LIS, its variance, and apparently the full distribution function appears in statistical analysis of some simple nonlinear stochastic partial differential equation

Longest increasing subsequence as expectation of a simple nonlinear stochastic PDE with a low noise intensity Lire la suite »

Level Density of a Bose Gas and Extreme Value Statistics

A. Comtet 1, 2, P. Leboeuf 1, Satya N. Majumdar 1 Physical Review Letters 98 (2007) 070404 We establish a connection between the level density of a gas of non-interacting bosons and the theory of extreme value statistics. Depending on the exponent that characterizes the growth of the underlying single-particle spectrum, we show that at a given excitation energy the limiting distribution

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Large Deviations of the Maximum Eigenvalue in Wishart Random Matrices

Pierpaolo Vivo 1, Satya N. Majumdar 2, Oriol Bohigas 2 Journal of Physics A: Mathematical and General 40 (2007) 4317-4337 We compute analytically the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x

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