Nonequilibrium scaling explorations on a 2D Z(5)-symmetric model

We have investigated the dynamic critical behavior of the two-dimensional Z(5)-symmetric spin model by using short-time Monte Carlo (MC) simulations. We have obtained estimates of some critical points in its rich phase diagram and included, among the usual critical lines the study of first-order (weak) transition by looking into the order-disorder phase transition. Besides, we also investigated the soft-disorder phase transition by considering empiric methods. A study of the behavior of $\beta /\nu z$ along the self-dual critical line has been performed and special attention has been devoted to the critical bifurcation point, or FZ (Fateev-Zamolodchikov) point. Firstly, by using a refinement method and taking into account simulations out-of-equilibrium, we were able to localize parameters of this point. In a second part of our study, we turned our attention to the behavior of the model at the early stage of its time evolution in order to find the dynamic critical exponent z as well as the static critical exponents $\beta$ and $$ of the FZ-point on square lattices. The values of the static critical exponents and parameters are in good agreement with the exact results, and the dynamic critical exponent $z\approx 2.28$ very close of the 4-state Potts model ($z\approx 2.29$).Comment: 11 pages, 7 figure

Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter $q$ to the inverse temperature $\beta$. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for $q=1$, which corresponds to the standard Metropolis algorithm. Non-locality implies in very time consuming computer calculations, since the energy of the whole system must be reevaluated, when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for Ising model. By using the short time non-equilibrium numerical simulations, we also calculate for this model: the critical temperature, the static and dynamical critical exponents as function of $q$. Even for $q\neq 1$, we show that suitable time evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results, when we use non-local dynamics, showing that short time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law considering in a log-log plot two successive refinements.Comment: 10 pages, 5 figures and 5 table

A new look at the 2D Ising model from exact partition function zeros for large lattice sizes

A general numerical method is presented to locate the partition function zeros in the complex beta plane for large lattice sizes. We apply this method to the 2D Ising model and results are reported for square lattice sizes up tp L=64. We also propose an alternative method to evaluate corrections to scaling which relies only on the leading zeros. This method is illustrated with our data.Comment: 9 pages, Latex, 3 figures. To appear in Int. J. Mod. Phys.

Thermodynamics on the spectra of random matrices

We show that the spectra of Wishart matrices built from magnetization time series can describe the phase transitions and the critical phenomena of the Potts model with a different number of states. We can statistically determine the transition points, independent of their order, by studying the density of the eigenvalues and corresponding fluctuations. In some way, we establish a relationship between the actual thermodynamics with the spectral thermodynamics described by the eigenvalues. The histogram of correlations between time series interestingly supports our results. In addition, we present an analogy to the study of the spectral properties of the Potts model, considering matrices correlated artificially. For such matrices, the eigenvalues are distributed in two groups that present a gap depending on such correlation.Comment: 10 pages, 11 figure

Stock Market Speculation: Spontaneous Symmetry Breaking of Economic Valuation

Firm foundation theory estimates a security's firm fundamental value based on four determinants: expected growth rate, expected dividend payout, the market interest rate and the degree of risk. In contrast, other views of decision-making in the stock market, using alternatives such as human psychology and behavior, bounded rationality, agent-based modeling and evolutionary game theory, expound that speculative and crowd behavior of investors may play a major role in shaping market prices. Here, we propose that the two views refer to two classes of companies connected through a ``phase transition''. Our theory is based on 1) the identification of the fundamental parity symmetry of prices ($p \to -p$), which results from the relative direction of payment flux compared to commodity flux and 2) the observation that a company's risk-adjusted growth rate discounted by the market interest rate behaves as a control parameter for the observable price. We find a critical value of this control parameter at which a spontaneous symmetry-breaking of prices occurs, leading to a spontaneous valuation in absence of earnings, similarly to the emergence of a spontaneous magnetization in Ising models in absence of a magnetic field. The low growth rate phase is described by the firm foundation theory while the large growth rate phase is the regime of speculation and crowd behavior. In practice, while large ``finite-time horizon'' effects round off the predicted singularities, our symmetry-breaking speculation theory accounts for the apparent over-pricing and the high volatility of fast growing companies on the stock markets.Comment: 23 pages, 10 figure

Not available

O modelo de Ashkin-Teller (1943) exibe um comportamento crítico, aparentemente não universal, semelhante ao do modelo de Baxter. Entretanto ele pode também ter propriedades críticas idênticas às do modelo de Ising, dependendo da relação entre as constantes de acoplamento. Nesse trabalho investigamos essas duas regiões de comportamento distinto, usando a hamiltoniana de tempo contínuo e, fazendo a hipótese de que esse limite não tira o sistema de sua classe de universalidade. Na região K4 ‹ K1 = K2 a hamiltoniana equivalente e uma versão discreta do modelo de Thirring massivo, e os índices críticos são calculados após a identificação das densidades com operadores desse modelo da teoria de campos. A região K4 ›K1 = K2, em que o modelo sofre duas transições, é estudada usando uma transformação do grupo de renormalização no espaço real. O modelo é reconhecido, nessa região, como sendo um modelo de Ising diluído que tem os expoentes usuaisThe Ashkin-Teller model (1943) displays non-universal critica1 behavior similar to the one found in the Baxter model. For appropriate values of the coupling constants it can, nevertheless, have critical properties identical to those found in the Ising model. In this work we study the entire phase diagram, and thus investigate both behaviours, using the continuous time hamiltonian. We assume that this limit preserves the universality class of the model. For K4‹ K1 = K2 the equivalent hamiltonian is a discrete version of the Thirring model, and critical indices are calculated after identification of the densities with operators of this field theoretical model. For K4› K1 = K2 the hamiltonian is equivalent to a dilute Ising model with the usual exponents. We also derive these exponents through a real space renormalization group transformatio

Not available

Os efeitos de confinamento por um potencial harmônico bi e tridimensional, nas propriedades magnéticas de um gás de elétrons livres, são investigados pelo uso da distribuição grand-canônica. No domínio de temperaturas altas uma extensão é feita aos trabalhos de Darwin e de Felderhof e Raval, para levar em conta efeitos de spin e verificar o limite de validade do seu procedimento. A baixas temperaturas o trabalho dá uma descrição abrangente das propriedades magnéticas do gás de elétrons , considerando o sistema finito mas sem introduzir as complicações oriundas da condição de contorno (ψ=0). São analisados os limite sem que a freqüência característica do potencial de confinamento (ω0) é muito maior ou muito menor do que a freqüência de Larmor (ωL) , correspondendo respectivamente aos casos de confinamento forte ou fraco, e suas implicações sobre o comportamento do momento magnético do sistemaThe effects of confinement by a two or three-dimensional harmonic potential on the rnagnetic properties of a free electron gas ate ivestigated by using the grand-canonical ensemble framework. At high temperatures an extension of Darwin\'s, Felderhof and Raval\'s works is made taking into account spin effects. At low temperatures this work gives a comprehensive description of the magnetic properties of a free electron gas. The system is regarded as finite, but the boundary condition (Ψ= 0) is not introduced. The limits of weak and strong confinement are also analyse