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

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

Partition function zeros and leading-order scaling correction of the 3D Ising model from multicanonical simulations

The density of states for the three-dimensional Ising model is calculated with high precision by means of multicanonical simulations. This allows us to estimate the leading partition function zeros for lattice sizes up to L = 32. We have evaluated the critical exponent ν and the correction to scaling through an analysis of a multi-parameter fit and of the Bulirsch-Stoer (BST) extrapolation algorithm. The performance of the BST algorithm is also explored in case of the 2D Ising model, where the exact partition function zeros are known