Search results for "Statistical"
showing 10 items of 4960 documents
Critical dynamics of long range models on Dynamical L\'evy Lattices
2023
We investigate critical equilibrium and out of equilibrium properties of a ferromagnetic Ising model in one and two dimension in the presence of long range interactions, $J_{ij}\propto r^{-(d+\sigma)}$. We implement a novel local dynamics on a dynamical L\'evy lattice, that correctly reproduces the static critical exponents known in the literature, as a function of the interaction parameter $\sigma$. Due to its locality the algorithm can be applied to investigate dynamical properties, of both discrete and continuous long range models. We consider the relaxation time at the critical temperature and we measure the dynamical exponent $z$ as a function of the decay parameter $\sigma$, highlight…
Transport and Scaling in Quenched 2D and 3D L\'evy Quasicrystals
2011
We consider correlated L\'evy walks on a class of two- and three-dimensional deterministic self-similar structures, with correlation between steps induced by the geometrical distribution of regions, featuring different diffusion properties. We introduce a geometric parameter $\alpha$, playing a role analogous to the exponent characterizing the step-length distribution in random systems. By a {\it single-long jump} approximation, we analytically determine the long-time asymptotic behavior of the moments of the probability distribution, as a function of $\alpha$ and of the dynamic exponent $z$ associated to the scaling length of the process. We show that our scaling analysis also applies to e…
The chiral Hall effect of magnetic skyrmions from a cyclic cohomology approach
2019
We demonstrate the emergence of an anomalous Hall effect in chiral magnetic textures which is neither proportional to the net magnetization nor to the well-known emergent magnetic field that is responsible for the topological Hall effect. Instead, it appears already at linear order in the gradients of the magnetization texture and exists for one-dimensional magnetic textures such as domain walls and spin spirals. It receives a natural interpretation in the language of Alain Connes' noncommutative geometry. We show that this chiral Hall effect resembles the familiar topological Hall effect in essential properties while its phenomenology is distinctly different. Our findings make the re-inter…
Scaling of the R\'enyi entropies in gapped quantum spin systems: Entanglement-driven order beyond symmetry breaking
2012
We investigate the scaling of the R\'enyi $\alpha$-entropies in one-dimensional gapped quantum spin models. We show that the block entropies with $\alpha > 2$ violate the area law monotonicity and exhibit damped oscillations. Depending on the existence of a factorized ground state, the oscillatory behavior occurs either below factorization or it extends indefinitely. The anomalous scaling corresponds to an entanglement-driven order that is independent of ground-state degeneracy and is revealed by a nonlocal order parameter defined as the sum of the single-copy entanglement over all blocks.
On the Sign Problem of the Fermionic Shadow Wave Function
2014
We present a whole series of novel methods to alleviate the sign problem of the Fermionic Shadow Wave Function in the context of Variational Monte Carlo. The effectiveness of our new techniques is demonstrated on the example of liquid 3He. We found that although the variance is substantially reduced, the gain in efficiency is restricted by the increased computational cost. Yet, this development not only extends the scope of the Fermionic Shadow Wave Function, but also facilitates highly accurate Quantum Monte Carlo simulations previously thought not feasible.
Percolation on correlated random networks
2011
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks themselves. Given the weighted nature of the graphs, different kinds of bond percolation can be studied: stochastic (deleting links randomly) and deterministic (deleting links based on rank weights), each mimicking a different physical process. The evolution of the network is accordingly different, as evidenced by the behavior of the largest component size and of the distribution of cluster sizes. In particular, we can derive that weak ties are crucial in o…
Organization and evolution of synthetic idiotypic networks
2012
We introduce a class of weighted graphs whose properties are meant to mimic the topological features of idiotypic networks, namely the interaction networks involving the B-core of the immune system. Each node is endowed with a bit-string representing the idiotypic specificity of the corresponding B cell and a proper distance between any couple of bit-strings provides the coupling strength between the two nodes. We show that a biased distribution of the entries in bit-strings can yield fringes in the (weighted) degree distribution, small-worlds features, and scaling laws, in agreement with experimental findings. We also investigate the role of ageing, thought of as a progressive increase in …
Quantum mechanics-classical molecular dynamics approach to EXAFS
2009
Recently developed approach to the simulation of configuration-averaged EXAFS spectra using the combination of quantum mechanics and classical Molecular Dynamics (MD) methods is presented on the example of the Ti K-edge in SrTiO3 at T = 300 K. The method allows one to significantly reduce the number of fitting parameters required in the EXAFS signal calculation and to account entirely for disorder contributions. We show also that the sensitivity of configuration-averaged EXAFS spectra to the force field model employed in the MD simulations allows one to use them as additional information for the force field parameters fitting.
Monte Carlo Simulations of Alloy Phase Transformations
1994
The use of Monte Carlo simulation methods for study of order-disorder phase transitions in lattice models of alloys is reviewed, with an emphasis on interfacial phenomena and the kinetics of ordering and/or phase separation. Topics discussed include the attempt to predict the phase diagram of Fe-Al alloys from recent measurements of effective interaction parameters, competition between magnetic and crystallographic ordering in such alloys, and the structure of their antiphase domain boundaries. Both an interfacial roughening transition of this domain wall and interfacial enrichment phenomena are predicted. Then simulations of alloy-vacuum surfaces are discussed, and it is shown that both ca…
Probabilities, States, Statistics
2016
In this chapter we clarify some important notions which are relevant in a statistical theory of heat: The definitions of probability measure, and of thermodynamic states are illustrated, successively, by the classical Maxwell-Boltzmann statistics, by Fermi-Dirac statistics and by Bose-Einstein statistics. We discuss observables and their eigenvalue spectrum as well as entropy and we calculate these quantities for some examples. The chapter closes with a comparison of statistical descriptions of classical and quantum gases.