Off-equilibrium relaxational dynamics with improved Ising Hamiltonian

We study the off-equilibrium relaxational dynamics at criticality in the three-dimensional Blume-Capel model whose static critical behaviour belongs to the 3d-Ising universality class. Using "improved" Hamiltonian (the leading corrections to scaling have vanishing amplitude) we perform Monte Carlo simulations of the relaxational dynamics after a quench from $T=\infty$ to $T_c$. Analysing the off-equilibrium dynamics at $T_c$ we obtain an estimate of the dynamical critical exponent $z=2.020(8)$ that is perfectly consistent with the Field Theory predictions.Comment: 14 pages, 7 figures, references added, to appear in J. Stat. Mec

Liquid-vapor transition of systems with mean field universality class

We have considered a system where the interaction, v(r) = v_IS(r) + xi^2 v_MF(r), is given as a linear combination of two potentials, each of which being characterized with a well-defined critical behavior: for v_IS(r) we have chosen the potential of the restricted primitive model which is known to belong to the Ising 3D (IS) universality class, while for v_MF(r) we have considered a long-range interaction in the Kac-limit, displaying mean field (MF) behavior. We study the performance of two theoretical approaches and of computer simulations in the critical region for this particular system and give a detailed comparison between theories and simulation of the critical region and the location of the critical point. Both, theory and simulation give evidence that the system belongs to the MF universality class for any positive value of xi and that it shows only non-classical behavior for xi=0. While in this limiting case theoretical approaches are known to fail, we find good agreement for the critical properties between the theoretical approaches and the simulations for xi^2 larger than 0.05.Comment: 9 pages, 11 figures, 3 table

A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class

We simulate the spin-1/2 Ising model and the Blume-Capel model at various values of the parameter D on the simple cubic lattice. We perform a finite size scaling study of lattices of a linear size up to L=360 to obtain accurate estimates for critical exponents. We focus on values of D, where the amplitudes of leading corrections are small. Furthermore we employ improved observables that have a small amplitude of the leading correction. We obtain nu=0.63002(10), eta=0.03627(10) and omega=0.832(6). We compare our results with those obtained from previous Monte Carlo simulations and high temperature series expansions of lattice models, by using field theoretic methods and experiments.Comment: 25 pages, 6 figures, typos corrected, references added, conclusions extende

Lyapunov Exponents for the Intermittent Transition to Chaos

The dependence of the Lyapunov exponent on the closeness parameter, $\epsilon$, in tangent bifurcation systems is investigated. We study and illustrate two averaging procedures for defining Lyapunov exponents in such systems. First, we develop theoretical expressions for an isolated tangency channel in which the Lyapunov exponent is defined on single channel passes. Numerical simulations were done to compare theory to measurement across a range of $\epsilon$ values. Next, as an illustration of defining the Lyapunov exponent on many channel passes, a simulation of the intermittent transition in the logistic map is described. The modified theory for the channels is explained and a simple model for the gate entrance rates is constructed. An important correction due to the discrete nature of the iterative flow is identified and incorporated in an improved model. Realistic fits to the data were made for the Lyapunov exponents from the logistic gate and from the full simulation. A number of additional corrections which could improve the treatment of the gates are identified and briefly discussed.Comment: 25 pages LaTeX and 12 separate ps figure

Universal amplitude ratios in the 3D Ising Universality Class

We compute a number of universal amplitude ratios in the three-dimensional Ising universality class. To this end, we perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. For example, we obtain A_+/A_-=0.536(2) and C_+/C_-=4.713(7), where A_+- and C_+- are the amplitudes of the specific heat and the magnetic susceptibility, respectively. The subscripts + and - indicate the high and the low temperature phase, respectively. We compare our results with those obtained from previous Monte Carlo simulations, high and low temperature series expansions, field theoretic methods and experiments.Comment: 18 pages, two figures, typos corrected, discussion on finite size corrections extende