Search results for "Statistical physics"
showing 10 items of 1402 documents
Partition function based analysis of cosmic microwave background maps
1999
We present an alternative method to analyse cosmic microwave background (CMB) maps. We base our analysis on the study of the partition function. This function is used to examine the CMB maps, making use of the different information embedded at different scales and moments. Using the partition function in a likelihood analysis in two dimensions (Qrms-PS, n), we find the best-fitting model to the best data available at present (the COBE–DMR 4 years data set). By means of this analysis we find a maximum in the likelihood function for n=1.8-0.65+0.35 and Qrms-PS = 10-2.5+3μ K (95 per cent confidence level) in agreement with the results of other similar analyses [Smoot et al. (1 yr), Bennet et a…
Dynamic percolation transition induced by phase separation: A Monte Carlo analysis
1987
The percolation transition of geometric clusters in the three-dimensional, simple cubic, nearest neighbor Ising lattice gas model is investigated in the temperature and concentration region inside the coexistence curve. We consider “quenching experiments,” where the system starts from an initially completely random configuration (corresponding to equilibrium at infinite temperature), letting the system evolve at the considered temperature according to the Kawasaki “spinexchange” dynamics. Analyzing the distributionnl(t) of clusters of sizel at timet, we find that after a time of the order of about 100 Monte Carlo steps per site a percolation transition occurs at a concentration distinctly l…
Suppression of noise in FitzHugh–Nagumo model driven by a strong periodic signal
2005
Abstract The response time of a neuron in the presence of a strong periodic driving in the stochastic FitzHugh–Nagumo model is investigated. We analyze two cases: (i) the variable that corresponds to membrane potential is subjected to fluctuations, and (ii) the recovery variable associated with the refractory properties of a neuron is noisy. The influence of noise sources on the delay of the response of a neuron is analyzed. In both cases we observe a resonant activation-like phenomenon and suppression of noise: the negative effect of fluctuations on the process of spike generation is minimal near the resonance region. The phenomenon of noise enhanced stability is also observed in both case…
Quantum fluctuations of the conductance in the hopping regime
1992
Abstract The results of the numerical scaling approach for localization are used to discuss the statistical behaviour of the zero-temperature conductance of disordered systems of finite size. In the asymptotic regime of strong localization, where transport is dominated by hopping processes, explicit expressions for the temperature dependence of the fluctuations of the conductance and the resistance are obtained by assuming that the phase coherence length is given by the Mott hopping law. It is shown that the temperature dependence of the fluctuations of the logarithm of the conductance/resistance does not depend on the assumptions concerning the statistics of the hopping processes. The resu…
Size effect in phase transition kinetics
1988
The growth of a spontaneous lattice average magnetization in a magnetic system which is suddenly brought below the transition temperature is a stochastic process in which the very small fluctuations of the initial magnetization are amplified to a macroscopic size. The initial magnetization fluctuates in time around the zero average value because of the finite size of the system. As a consequence of the fluctuation-amplification phenomenon the nonlinear relaxation of the finite system is qualitatively different from that of the infinite one. The present paper studies this feature of phase-transition kinetics in the framework of a very simple model: the dynamical generalization of the spheric…
Dynamical coexistence in moderately polydisperse hard-sphere glasses
2020
We perform extensive numerical simulations of a paradigmatic model glass former, the hard-sphere fluid with 10% polydispersity. We sample from the ensemble of trajectories with fixed observation time, whereby single trajectories are generated by event-driven molecular dynamics. We show that these trajectories can be characterized in terms of the local structure, and we find a dynamical-structural (active-inactive) phase transition between two dynamical phases: one dominated by liquidlike trajectories with a low degree of local order and one dominated by glassylike trajectories with a high degree of local order. We show that both phases coexist and are separated by a spatiotemporal interface…
Some Important Recent Developments of the Monte Carlo Methodology
2002
Roughly at the time (1987) when the manuscript for the first three chapters of the present book was completed, several breakthroughs occurred. They had a profound influence on the scope of Monte Carlo simulations in statistical physics, particularly for the study of phase transitions in lattice models.
Statistical properties of the eigenvalue spectrum of the three-dimensional Anderson Hamiltonian
1993
A method to describe the metal-insulator transition (MIT) in disordered systems is presented. For this purpose the statistical properties of the eigenvalue spectrum of the Anderson Hamiltonian are considered. As the MIT corresponds to the transition between chaotic and nonchaotic behavior, it can be expected that the random matrix theory enables a qualitative description of the phase transition. We show that it is possible to determine the critical disorder in this way. In the thermodynamic limit the critical point behavior separates two different regimes: one for the metallic side and one for the insulating side.
Monte Carlo tests of renormalization-group predictions for critical phenomena in Ising models
2001
Abstract A critical review is given of status and perspectives of Monte Carlo simulations that address bulk and interfacial phase transitions of ferromagnetic Ising models. First, some basic methodological aspects of these simulations are briefly summarized (single-spin flip vs. cluster algorithms, finite-size scaling concepts), and then the application of these techniques to the nearest-neighbor Ising model in d=3 and 5 dimensions is described, and a detailed comparison to theoretical predictions is made. In addition, the case of Ising models with a large but finite range of interaction and the crossover scaling from mean-field behavior to the Ising universality class are treated. If one c…
SCALING THEORY AND THE CLASSIFICATION OF PHASE TRANSITIONS
1992
The recent classification theory for phase transitions (R. Hilfer, Physica Scripta 44, 321 (1991)) and its relation with the foundations of statistical physics is reviewed. First it is outlined how Ehrenfests classification scheme can be generalized into a general thermodynamic classification theory for phase transitions. The classification theory implies scaling and multiscaling thereby eliminating the need to postulate the scaling hypothesis as a fourth law of thermodynamics. The new classification has also led to the discovery and distinction of nonequilibrium transitions within equilibrium statistical physics. Nonequilibrium phase transitions are distinguished from equilibrium transiti…