Fluctuation-dissipation relations and field-free algorithms for the computation of response functions

We discuss the relation between the fluctuation-dissipation relation derived by Chatelain and Ricci-Tersenghi [C.Chatelain, J.Phys. A {\bf 36}, 10739 (2003); F. Ricci-Tersenghi, Phys.Rev.E 68, 065104(R) (2003)] and that by Lippiello-Corberi-Zannetti [E. Lippiello, F. Corberi and M. Zannetti Phys. Rev. E {\bf 72}, 056103 (2005)]. In order to do that, we re-derive the fluctuation-dissipation relation for systems of discrete variables evolving in discrete time via a stochastic non-equilibrium Markov process. The calculation is carried out in a general formalism comprising the Chatelain, Ricci-Tersenghi result and that by Lippiello-Corberi-Zannetti as special cases. The applicability, generality, and experimental feasibility of the two approaches is thoroughly discussed. Extending the analytical calculation to the variance of the response function we show the vantage of field-free numerical methods with respect to the standard method where the perturbation is applied. We also show that the signal to noise ratio is better (by a factor $\sqrt 2$) in the algorithm of Lippiello-Corberi-Zannetti with respect to that of Chatelain-Ricci Tersenghi.Comment: 17 pages, 5 figures. To appear in Phys. Rev.

Numerical evidence of the double-Griffiths phase of the random quantum Ashkin-Teller chain

The random quantum Ashkin-Teller chain is studied numerically by means of time-dependent Density-Matrix Renormalization Group. The critical lines are estimated as the location of the peaks of the integrated autocorrelation times, computed from spin-spin and polarization-polarization autocorrelation functions. Disorder fluctuations of magnetization and polarization are observed to be maximum on these critical lines. Entanglement entropy leads to the same phase diagram, though with larger Finite-Size effects. The decay of spin-spin and polarization-polarization autocorrelation functions provides numerical evidence of the existence of a double Griffiths phase when taking into account finite-size effects. The two associated dynamical exponents z increase rapidly as the critical lines are approached, in agreement with the recent conjecture of a divergence at the two transitions in the thermodynamic limit

Change detection in multisensor SAR images using bivariate gamma distributions

This paper studies a family of distributions constructed from multivariate gamma distributions to model the statistical properties of multisensor synthetic aperture radar (SAR) images. These distributions referred to as multisensor multivariate gamma distributions (MuMGDs) are potentially interesting for detecting changes in SAR images acquired by different sensors having different numbers of looks. The first part of the paper compares different estimators for the parameters of MuMGDs. These estimators are based on the maximum likelihood principle, the method of inference function for margins and the method of moments. The second part of the paper studies change detection algorithms based on the estimated correlation coefficient of MuMGDs. Simulation results conducted on synthetic and real data illustrate the performance of these change detectors

Second-Order Phase Transition Induced by Deterministic Fluctuations in Aperiodic Eight-State Potts Models

We investigate the influence of aperiodic modulations of the exchange interactions between nearest-neighbour rows on the phase transition of the two-dimensional eight-state Potts model. The systems are studied numerically through intensive Monte Carlo simulations using the Swendsen-Wang cluster algorithm for different aperiodic sequences. The transition point is located through duality relations, and the critical behaviour is investigated using FSS techniques at criticality. While the pure system exhibits a first-order transition, we show that the deterministic fluctuations resulting from the aperiodic coupling distribution are liable to modify drastically the physical properties in the neighbourhood of the transition point. For strong enough fluctuations of the sequence under consideration, a second-order phase transition is induced. The exponents $\beta/\nu$, $\gamma /\nu$ and $(1-\alpha)/\nu$ are obtained at the new fixed point and crossover effects are discussed. Surface properties are also studied.Comment: LaTeX file with EPJB macro package, 11 pages, 16 postscript figures, to appear in Eur. Phys. J.

Bivariate Gamma Distributions for Image Registration and Change Detection

This paper evaluates the potential interest of using bivariate gamma distributions for image registration and change detection. The first part of this paper studies estimators for the parameters of bivariate gamma distributions based on the maximum likelihood principle and the method of moments. The performance of both methods are compared in terms of estimated mean square errors and theoretical asymptotic variances. The mutual information is a classical similarity measure which can be used for image registration or change detection. The second part of the paper studies some properties of the mutual information for bivariate Gamma distributions. Image registration and change detection techniques based on bivariate gamma distributions are finally investigated. Simulation results conducted on synthetic and real data are very encouraging. Bivariate gamma distributions are good candidates allowing us to develop new image registration algorithms and new change detectors

Quenched bond dilution in two-dimensional Potts models

We report a numerical study of the bond-diluted 2-dimensional Potts model using transfer matrix calculations. For different numbers of states per spin, we show that the critical exponents at the random fixed point are the same as in self-dual random-bond cases. In addition, we determine the multifractal spectrum associated with the scaling dimensions of the moments of the spin-spin correlation function in the cylinder geometry. We show that the behaviour is fully compatible with the one observed in the random bond case, confirming the general picture according to which a unique fixed point describes the critical properties of different classes of disorder: dilution, self-dual binary random-bond, self-dual continuous random bond.Comment: LaTeX file with IOP macros, 29 pages, 14 eps figure