A.M. Mariz

On the irreversible nature of the Tsallis and Renyi entropies

Abstract We prove that the detailed balance hypothesis (i.e., Aij=Aji, where {Aij} are the transition probabilities, per unit time, between any two microscopic configurations i and j) implies irreversibility of both the recently introduced Tsallis entropy STq≡ [k/(q−1)](1−Σwi=1Pqi) as well as the Renyi entropy S R q ≡[k/(1−q)]ln(Σ w i=1 P q i )(qϵ R . More precisely, for q>0, Q=0and q

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.

Spin wave specific heat in quasiperiodic Fibonacci structures

The energy spectra of a variety of collective modes on quasiperiodic structures exhibit a complex fractal profile. Among the modes that have attracted particular attention in this context are the spin wave spectra of quasiperiodic magnetic multilayers that obey a substitutional sequence of the Fibonacci type. They are described within the framework of the Heisenberg theory. In order to have a deep insight on the relevant thermodynamical implications of the above mentioned energy spectras fractal profile, we have performed analytical and numerical calculations of the spin wave specific heat associated with successive hierarchical sequences of the Fibonacci quasiperiodic structures. The spectra show interesting oscillatory behavior in the low-temperature region, which can be traced back to the spin waves self-similar energy spectrum.

Unified long-memory mesoscopic mechanism consistent with nonextensive statistical mechanics

Abstract We unify two long-memory Fokker–Planck mechanisms. Stationary solutions of the equation ∂ p ( x , t ) ∂ t = − ∂ ∂ x [ F ( x ) p ( x , t ) ] + 1 2 D ∂ 2 ∂ x 2 [ ϕ ( x , p ) p ( x , t ) ] ( D ∈ R ; F ( x ) = − ∂ V ( x ) / ∂ x ) exist for a wide class of systems, namely for ϕ ( x , p ) = [ A + B V ( x ) ] θ [ p ( x , t ) ] η , ( A , B , θ , η ) being constants. We obtain that, for θ ≠ 1 and arbitrary confining potential V ( x ) , p ( x , ∞ ) ∝ { 1 − β ( 1 − q ) V ( x ) } 1 / ( 1 − q ) ≡ e q − β V ( x ) , where q = 1 + η / ( θ − 1 ) .

The anisotropic Ashkin–Teller model: a renormalization group study

The two-dimensional ferromagnetic anisotropic Ashkin–Teller model is investigated through a real-space renormalization-group approach. The critical frontier, separating five distinct phases, recovers all the known exact results for the square lattice. The correlation length (νT) and crossover (φ) critical exponents are also calculated. With the only exception of the four-state Potts critical point, the entire phase diagram belongs to the Ising universality class.

Transmission fingerprints in quasiperiodic magnetic structures

In this paper we study the spin wave transmission spectra of quasiperiodic magnetic multilayers following Fibonacci, double period and Thue–Morse sequences. We consider multilayers that are composed of two simple cubic ferromagnetic materials surrounded by two semi-infinite slabs of a third ferromagnetic material. A transfer matrix treatment is employed with the calculations carried out for the exchange-dominated regime within the framework of the Heisenberg model and taking into account the random phase approximation. The numerical results illustrate the self-similar aspects of the spectra as well as their magnetic transmission fingerprints, which can be used to identify the sequence applied to construct the system.

The two-dimensional site-diluted Ising ferromagnet a damage-spreading analysis

The quenched site-diluted Ising ferromagnet on a square lattice, for which each site is occupied or empty with probabilities p and 1 − p, respectively, is studied numerically through damage-spreading procedures. By making use of the Glauber dynamics, the percolation threshold pc is estimated. Within the heat-bath dynamics, the damage-spreading temperatures Td(p) (for several values of p>pc) are computed, indicating a strong correlation with the corresponding critical temperatures Tc(p). A procedure for estimating the fractal dimensions of clusters of damaged sites, at low temperatures, is presented; as p → pc, our estimate is very close to 91/48, which is the fractal dimension of the infinite cluster at p = pc in two-dimensional site percolation. Whenever possible to compare, our results are in good agreement with the best estimates available from other techniques, in spite of a modest computational effort.

The three-dimensional quantum Heisenberg ferromagnet with random anisotropy

The authors study the critical properties of the 3D quantum Heisenberg ferromagnet with random anisotropies; that is, the coupling between any pair of nearest-neighbouring spins can be either isotropic (Heisenberg) or anisotropic (Ising-or XY-like) at random. Within a Migdal-Kadanoff approximation they obtain the full critical frontier and correlation length critical exponents. They found that the isotropic Heisenberg model is unstable (in the context of universality classes) in the presence of a small concentration of couplings with lower symmetry.

Z(6) model: Criticality and break-collapse method

Abstract The phase diagram and thermal and crossover exponents of the Z(6) ferromagnet on the square lattice are calculated within a real-space renormalization group (RG) scheme. The obtained phase diagram (exhibiting 4 phases corresponding to Z(6), Z(3), Z(2) and completely broken symmetries) contains all exactly known critical points, and possibly is an excellent approximation everywhere except in the high-temperature region where a soft phase is expected to appear. However, all the obtained results are exact in the Wheatstone-bridge hierarchical lattice. In addition to these results, we present an operational procedure (the “break-collapse method”) which considerably simplifies the exact calculation of two-spin correlation functions for arbitrary Z(6) two-rooted clusters (frequent in RG approaches).

Damage spreading in the (Nα,Nβ) model: exact results

The (Nα,Nβ) model is investigated within the damage-spreading framework. Exact relations involving thermodynamic quantities (order parameters and correlation functions) and conveniently defined combinations of damages are obtained, which are valid for any regular (translationally invariant) lattice. The corresponding existing results for particular cases of the model, e.g., Ising, Potts, Ashkin–Teller and discrete N-vector models, are all recovered by the present relations.