Short Range Ising Spin Glasses: a critical exponent study

The critical properties of short-range Ising spin-glass models, defined on a diamond hierarchical lattice of graph fractal dimension $d_{f}=2.58$, 3, and 4, and scaling factor 2 are studied via a method based on the Migdal-Kadanoff renormalization-group scheme. The order parameter critical exponent $\beta$ is directly estimated from the data of the local Edwards- Anderson (EA) order parameter, obtained through an exact recursion procedure. The scaling of the EA order parameter, leading to estimates of the $\nu$ exponent of the correlation length is also performed. Four distinct initial distributions of the quenched coupling constants (Gaussian, bimodal, uniform and exponential) are considered. Deviations from a universal behaviour are observed and analysed in the framework of the renormalized flow in a two dimensional appropriate parameter space.Comment: 9 pages, 01 figure (ps

Universality in short-range Ising spin glasses

The role of the distribution of coupling constants on the critical exponents of the short-range Ising spin-glass model is investigated via real space renormalization group. A saddle-point spin glass critical point characterized by a fixed-point distribution is found in an appropriated parameter space. The critical exponents $\beta$ and $\nu$ are directly estimated from the data of the local Edwards-Anderson order parameters for the model defined on a diamond hierarchical lattice of fractal dimension $d_{f}=3$. Four distinct initial distributions of coupling constants (Gaussian, bimodal, uniform and exponential) are considered; the results clearly indicate a universal behavior.Comment: 11 pages, 4 figures, to published in Physica A 199

On the equivalence of the Ashkin-Teller and the four-state Potts-glass models of neural networks

We show that for a particular choice of the coupling parameters the Ashkin-Teller spin-glass neural network model with the Hebb learning rule and one condensed pattern yields the same thermodynamic properties as the four-state anisotropic Potts-glass neural network model. This equivalence is not seen at the level of the Hamiltonians.Comment: 3 pages, revtex, additional arguments presente

A p-Spin Interaction Ashkin-Teller Spin-Glass Model

A p-spin interaction Ashkin-Teller spin glass, with three independent Gaussian probability distributions for the exchange interactions, is studied by means of the replica method. A simple phase diagram is obtained within the replica-symmetric approximation, presenting an instability of the paramagnetic solution at low temperatures. The replica-symmetry-breaking procedure is implemented and a rich phase diagram is obtained; besides the paramagnetic phase, three distinct spin-glass phases appear. Three first-order critical frontiers are found and they all meet at a triple point; among such lines, two of them present discontinuities in the order parameters, but no latent heat, whereas the other one exhibits both discontinuities in the order parameters and a finite latent heat.Comment: 17 pages, 2 figures, submitted to Physica

Damage Spreading During Domain Growth

We study damage spreading in models of two-dimensional systems undergoing first order phase transitions. We consider several models from the same non-conserved order parameter universality class, and find unexpected differences between them. An exact solution of the Ohta-Jasnow-Kawasaki model yields the damage growth law $D \sim t^{\phi}$, where $\phi = t^{d/4}$ in $d$ dimensions. In contrast, time-dependent Ginzburg-Landau simulations and Ising simulations in $d= 2$ using heat-bath dynamics show power-law growth, but with an exponent of approximately $0.36$, independent of the system sizes studied. In marked contrast, Metropolis dynamics shows damage growing via $\phi \sim 1$, although the damage difference grows as $t^{0.4}$. PACS: 64.60.-i, 05.50.+qComment: 4 pags of revtex3 + 3 postscript files appended as a compressed and uuencoded file. UIB940320

Comment on "Critique of q-entropy for thermal statistics" by M. Nauenberg

It was recently published by M. Nauenberg [1] a quite long list of objections about the physical validity for thermal statistics of the theory sometimes referred to in the literature as {\it nonextensive statistical mechanics}. This generalization of Boltzmann-Gibbs (BG) statistical mechanics is based on the following expression for the entropy: S_q= k\frac{1- \sum_{i=1}^Wp_i^q}{q-1} (q \in {\cal R}; S_1=S_{BG} \equiv -k\sum_{i=1}^W p_i \ln p_i) . The author of [1] already presented orally the essence of his arguments in 1993 during a scientific meeting in Buenos Aires. I am replying now simultaneously to the just cited paper, as well as to the 1993 objections (essentially, the violation of "fundamental thermodynamic concepts", as stated in the Abstract of [1]).Comment: 7 pages including 2 figures. This is a reply to M. Nauenberg, Phys. Rev. E 67, 036114 (2003

Histological and ultrastructural feature and nitrite production of caprine preantral follicles in vitro cultured in the presence or absence of serum

Avaliou-se o efeito da adição de diferentes tipos e concentrações de soro sobre o desenvolvimento e a sobrevivência de folículos ovarianos pré-antrais (FOPA) caprinos in vitro. Além disso, verificou-se a relação entre as concentrações de nitrito presentes no meio de cultivo e a viabilidade folicular. Cada par ovariano foi dividido em 29 fragmentos, sendo um destinado ao controle. Os fragmentos foram cultivados por um ou sete dias em meio essencial mínimo suplementado (MEM+) ou MEM+ com diferentes concentrações (10 ou 20%) de soro fetal bovino (SFB), soro de cabra em estro (SCE) ou soro de cabra em diestro (SCD). Na análise morfológica após sete dias, apenas o tratamento com 10% de SFB apresentou percentual de FOPA normais similar ao MEM+ (P>0,05). A análise ultra-estrutural dos folículos cultivados por sete dias com MEM+ ou MEM+ com 10% de SFB mostrou danos oocitários, porém células da granulosa normais. A análise do meio de cultivo revelou correlação positiva entre a viabilidade folicular e a produção de nitrito. A suplementação com soro não melhorou a viabilidade de FOPA e a concentração de nitrito no meio de cultivo funcionou como um indicador da viabilidade das células da granulosa de FOPA caprinos cultivados in vitro. ______________________________________________________________________________________________________________ ABSTRACTThe effect of the addition of different types and concentrations of sera on the viability and development of caprine preantal follicles (PAF) in vitro cultured was analyzed. In addition, it was evaluated the correlation between nitrite concentrations in culture medium and folicular viability. Each ovarian pair was divided in 29 fragments and one was used as control. The fragments were cultured for one or seven days in minimal essential medium (MEM+) or MEM+ with different concentrations of (10 or 20%) bovine fetal serum (BFS), estrous goat serum (EGS), or diestrous goat serum (DGS). After seven days, the morphological analysis showed that only the treatment with 10% BFS maintained the percentage of normal PAF similar to MEM+ (P>0.05). The ultrastructural analysis of follicles cultured for seven days in MEM+ or MEM+ with 10% BFS showed some oocyte damage, although the granulosa cells were normal. Analysis of culture medium revealed a positive correlation between follicular viability and nitrite production. Supplementation with serum did not improve the viability of PAF and nitrite levels in culture medium served as an indicator of viability of granulose cells from caprine PAF in vitro cultured

Black hole thermodynamical entropy

As early as 1902, Gibbs pointed out that systems whose partition function diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs (BG) theory. Consistently, since the pioneering Bekenstein-Hawking results, physically meaningful evidence (e.g., the holographic principle) has accumulated that the BG entropy $S_{BG}$ of a $(3+1)$ black hole is proportional to its area $L^2$ ($L$ being a characteristic linear length), and not to its volume $L^3$. Similarly it exists the \emph{area law}, so named because, for a wide class of strongly quantum-entangled $d$-dimensional systems, $S_{BG}$ is proportional to $\ln L$ if $d=1$, and to $L^{d-1}$ if $d>1$, instead of being proportional to $L^d$ ($d \ge 1$). These results violate the extensivity of the thermodynamical entropy of a $d$-dimensional system. This thermodynamical inconsistency disappears if we realize that the thermodynamical entropy of such nonstandard systems is \emph{not} to be identified with the BG {\it additive} entropy but with appropriately generalized {\it nonadditive} entropies. Indeed, the celebrated usefulness of the BG entropy is founded on hypothesis such as relatively weak probabilistic correlations (and their connections to ergodicity, which by no means can be assumed as a general rule of nature). Here we introduce a generalized entropy which, for the Schwarzschild black hole and the area law, can solve the thermodynamic puzzle.Comment: 7 pages, 2 figures. Accepted for publication in EPJ

Thermodynamic Description of the Relaxation of Two-Dimensional Euler Turbulence Using Tsallis Statistics

Euler turbulence has been experimentally observed to relax to a metaequilibrium state that does not maximize the Boltzmann entropy, but rather seems to minimize enstrophy. We show that a recent generalization of thermodynamics and statistics due to Tsallis is capable of explaining this phenomenon in a natural way. The maximization of the generalized entropy $S_{1/2}$ for this system leads to precisely the same profiles predicted by the Restricted Minimum Enstrophy theory of Huang and Driscoll. This makes possible the construction of a comprehensive thermodynamic description of Euler turbulence.Comment: 15 pages, RevTe