O Modelo de Ising inomogêneo: uma interrupção contínua entre as redes quadrada e triangular.

The ferromagnetic and antiferromagnetic Ising model on a two dimensional inhomogeneous lattice characterized by two exchange constants (J1 and J2) is investigated. The lattice allows, in a continuous manner, the interpolation between the uniforme square (J2 = 0) and triangular (J2 = J1) lattices. By performing Monte Carlo simulation using the sequential Metropolis algorithm, we calculate the magnetization and the magnetic susceptibility on lattices of differents sizes. Applying the finite size scaling method through a data colappse, we obtained the critical temperatures as well as the critical exponents of the model for several values of the parameter α = J2 J1 in the [0, 1] range. The ferromagnetic case shows a linear increasing behavior of the critical temperature Tc for increasing values of α. Inwhich concerns the antiferromagnetic system, we observe a linear (decreasing) behavior of Tc, only for small values of α; in the range [0.6, 1], where frustrations effects are more pronunciated, the critical temperature Tc decays more quickly, possibly in a non-linear way, to the limiting value Tc = 0, cor-responding to the homogeneous fully frustrated antiferromagnetic triangular case.

Propagação de danos no modelo de ising em redes de bravais e em fractais

In this work we have studied, by Monte Carlo computer simulation, several properties that characterize the damage spreading in the Ising model, defined in Bravais lattices (the square and the triangular lattices) and in the Sierpinski Gasket. First, we investigated the antiferromagnetic model in the triangular lattice with uniform magnetic field, by Glauber dynamics; The chaotic-frozen critical frontier that we obtained coincides , within error bars, with the paramegnetic-ferromagnetic frontier of the static transition. Using heat-bath dynamics, we have studied the ferromagnetic model in the Sierpinski Gasket: We have shown that there are two times that characterize the relaxation of the damage: One of them satisfy the generalized scaling theory proposed by Henley (critical exponent z~A/T for low temperatures). On the other hand, the other time does not obey any of the known scaling theories. Finally, we have used methods of time series analysis to study in Glauber dynamics, the damage in the ferromagnetic Ising model on a square lattice. We have obtained a Hurst exponent with value 0.5 in high temperatures and that grows to 1, close to the temperature TD, that separates the chaotic and the frozen phases

Estudo de propriedades críticas em sistemas complexos: método de procura automática em sistemas tipo Ising e percolação de longo alcance

The new technique for automatic search of the order parameters and critical properties is applied to several well-know physical systems, testing the efficiency of such a procedure, in order to apply it for complex systems in general. The automatic-search method is combined with Monte Carlo simulations, which makes use of a given dynamical rule for the time evolution of the system. In the problems inves¬tigated, the Metropolis and Glauber dynamics produced essentially equivalent results. We present a brief introduction to critical phenomena and phase transitions. We describe the automatic-search method and discuss some previous works, where the method has been applied successfully. We apply the method for the ferromagnetic fsing model, computing the critical fron¬tiers and the magnetization exponent (3 for several geometric lattices. We also apply the method for the site-diluted ferromagnetic Ising model on a square lattice, computing its critical frontier, as well as the magnetization exponent f3 and the susceptibility exponent 7. We verify that the universality class of the system remains unchanged when the site dilution is introduced. We study the problem of long-range bond percolation in a diluted linear chain and discuss the non-extensivity questions inherent to long-range-interaction systems. Finally we present our conclusions and possible extensions of this work

Simulações de Monte Carlo para os modelos Ising e Blume-Capel em redes complexa

We studied the Ising model ferromagnetic as spin-1/2 and the Blume-Capel model as spin-1, > 0 on small world network, using computer simulation through the Metropolis algorithm. We calculated macroscopic quantities of the system, such as internal energy, magnetization, specific heat, magnetic susceptibility and Binder cumulant. We found for the Ising model the same result obtained by Koreans H. Hong, Beom Jun Kim and M. Y. Choi [6] and critical behavior similar Blume-Capel model

Propagação de danos em sistemas cooperativos: propriedades termodinâmicas

High-precision calculations of the correlation functions and order parameters were performed in order to investigate the critical properties of several two-dimensional ferro- magnetic systems: (i) the q-state Potts model; (ii) the Ashkin-Teller isotropic model; (iii) the spin-1 Ising model. We deduced exact relations connecting specific damages (the difference between two microscopic configurations of a model) and the above mentioned thermodynamic quanti- ties which permit its numerical calculation, by computer simulation and using any ergodic dynamics. The results obtained (critical temperature and exponents) reproduced all the known values, with an agreement up to several significant figures; of particular relevance were the estimates along the Baxter critical line (Ashkin-Teller model) where the exponents have a continuous variation. We also showed that this approach is less sensitive to the finite-size effects than the standard Monte-Carlo method. This analysis shows that the present approach produces equal or more accurate results, as compared to the usual Monte Carlo simulation, and can be useful to investigate these models in circumstances for which their behavior is not yet fully understood

Modelo de ashkin-teller de três cores na rede ponte de wheatstone

In this work we study the phase transitions of the ferromagnetic three-color Ashkin-Teller Model in the hierarquical lattice generated by the Wheatstone bridge using real space renormalization group approach. With such technique we obtain the phase diagram and its critical points with respective critical exponents v. This model presents four phases: ferromagnetic, paramagnetic and two intermediates. Nine critical points were found, three of which are of Ising model type, three are of four states Potts model type, one is of eight states Potts model type and the last two which do not correspond to any Potts model with integer number of states. iv