P. M. C. de Oliveira

Broad histogram Monte Carlo

Abstract:We propose a new Monte Carlo technique in which the degeneracy of energy states is obtained with a Markovian process analogous to that of Metropolis used currently in canonical simulations. The obtained histograms are much broader than those of the canonical histogram technique studied by Ferrenberg and Swendsen. Thus we can reliably reconstruct thermodynamic functions over a much larger temperature scale also away from the critical point. We show for the two-dimensional Ising model how our new method reproduces exact results more accurately and using less computer time than the conventional histogram method. We also show data in three dimensions for the Ising ferromagnet and the Edwards Anderson spin glass.

Broad histogram relation is exact

Abstract:The Broad Histogram is a method designed to calculate the energy degeneracy g(E) from microcanonical averages of certain macroscopic quantities N up and N dn. These particular quantities are defined within the method, and their averages must be measured at constant energy values, i.e. within the microcanonical ensemble. Monte-Carlo simulational methods are used in order to perform these measurements. Here, the mathematical relation allowing one to determine g(E) from these averages is shown to be exact for any statistical model, i.e. any energy spectrum, under completely general conditions. We also comment about some troubles concerning the measurement of the quoted microcanonical averages, when one uses a particular approach, namely the energy random walk dynamics. These troubles appear when movements corresponding to different energy jumps are performed using the same probability, and also when the correlations between successive averaging states are not adequately treated: they have nothing to do with the method itself.The Broad Histogram is a method designed to calculate the energy degeneracy g(E) from microcanonical averages of certain macroscopic quantities N up and N dn. These particular quantities are defined within the method, and their averages must be measured at constant energy values, i.e. within the microcanonical ensemble. Monte-Carlo simulational methods are used in order to perform these measurements. Here, the mathematical relation allowing one to determine g(E) from these averages is shown to be exact for any statistical model, i.e. any energy spectrum, under completely general conditions. We also comment about some troubles concerning the measurement of the quoted microcanonical averages, when one uses a particular approach, namely the energy random walk dynamics. These troubles appear when movements corresponding to different energy jumps are performed using the same probability, and also when the correlations between successive averaging states are not adequately treated: they have nothing to do with the method itself.

Monte Carlo simulations of sexual reproduction

Modifying the Redfield model of sexual reproduction and the Penna model of biological aging, we compare reproduction with and without recombination in age-structured populations. In constrast to Redfield and in agreement with Bernardes we find sexual reproduction to be preferred to asexual one. In particular, the presence of old but still reproducing males helps the survival of younger females beyond their reproductive age.

Finite-Size Scaling Renormalization Group

A renormalization group approach based only on the finite-size scaling hypothesis, with no further assumptions, is presented. It is applied, as an example, to the 2D and 3D Ising ferromagnet in a uniform field. The critical behaviour of this system is discussed in detail, not only around the critical point (J = J0 and H = 0), but also around both the ferromagnetic (J → ∞ and H = 0) and paramagnetic (J = 0 and H = 0) points. All physical features of the system are successfully described, both qualitatively as well as quantitatively.

Long-range anticorrelations and non-Gaussian behavior of a leaky faucet

We find that intervals between successive drops from a leaky faucet display scale-invariant, long-range anticorrelations characterized by the same exponents of heart beat-to-beat intervals of healthy subjects. This behavior is also confirmed by numerical simulations on lattice and it is faucet-width- and flow-rate-independent. The histogram for the drop intervals is also well described by a Levy distribution with the same index for both histograms of healthy and diseased subjects. This additional result corroborates the evidence for similarities between leaky faucets and healthy hearts underlying dynamics.

THE SPIN-S BLUME-CAPEL RG FLOW DIAGRAM

Using the finite-size scaling renormalization group, we obtain the two-dimensional flow diagram of the Blume-Capel model forS=1 andS=3/2. In the first case our results are similar to those of mean-field theory, which predicts the existence of first- and second-order transitions with a tricritical point. In the second case, however, our results are different. While we obtain in theS=1 case a phase diagram presenting a multicritical point, the mean-field approach predicts only a second-order transition and a critical endpoint.

Stable spins in the zero temperature spinodal decomposition of 2D Potts models

We present the results of zero temperature Monte Carlo simulations of the q-state Potts model on a square lattice with either four or eight neighbors, and for the triangular lattice with six neighbors. In agreement with previous works, we observe that the domain growth process gets blocked for the nearest-neighbor square lattice when q is large enough, whereas for the eight neighbor square lattice and for the triangular lattice no blocking is observed. Our simulations indicate that the number of spins which never flipped from the beginning of the simulation up to time t follows a power law as a function of the energy, even in the case of blocking. The exponent of this power law varies from less than sol12 for the Ising case (1q = 2) to 2 for q → ∞ and seems to be universal. The effect of blocking on this exponent is invisible at least up to q = 7.

Transmission fingerprints of quasi-periodic chains

We propose a method to characterize quasi-periodic chains, based on the transmission probabilities. We consider finite layers which are building up following the Fibonaci, Thue-Morse and Cantor sequences. The spectra show an undoubtedly fractal behavior, with a distinct appearence for each chain. Furthermore, we construct return maps which present the same characteristic attractor for all peaks of energies within the same kind of chain.

Renormalization group studies of the Ashkin-Teller model

The two-and-three-dimensional Ashkin-Teller model is studied within two renormalization group treatments. The complete flow diagram is obtained for this two-parameter Hamiltonian and the results for the critical couplings and critical exponents are compared to the exact ones when avaible.

Simulating the complex behavior of a leaky faucet

The complex behavior of leaky faucets is obtained by numerical simulation using a stochastic method introduced by Mannaet al. and the results are compared with experimental data. Typical return maps of thin faucets are reproduced.