Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero-and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent a of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

Characterization of dynamic speckle sequences using principal component analysis and image descriptors

Speckle is being used as a characterization tool for the analysis of the dynamic of slow varying phenomena occurring in biological and industrial samples. The retrieved data takes the form of a sequence of speckle images. The analysis of these images should reveal the inner dynamic of the biological or physical process taking place in the sample. Very recently, it has been shown that principal component analysis is able to split the original data set in a collection of classes. These classes can be related with the dynamic of the observed phenomena. At the same time, statistical descriptors of biospeckle images have been used to retrieve information on the characteristics of the sample. These statistical descriptors can be calculated in almost real time and provide a fast monitoring of the sample. On the other hand, principal component analysis requires longer computation time but the results contain more information related with spatial-temporal pattern that can be identified with physical process. This contribution merges both descriptions and uses principal component analysis as a pre-processing tool to obtain a collection of filtered images where a simpler statistical descriptor can be calculated. The method has been applied to slow-varying biological and industrial processes