The hexatic phase of the two-dimensional hard disks system

We report Monte Carlo results for the two-dimensional hard disk system in the transition region. Simulations were performed in the NVT ensemble with up to 1024^2 disks. The scaling behaviour of the positional and bond-orientational order parameter as well as the positional correlation length prove the existence of a hexatic phase as predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young theory. The analysis of the pressure shows that this phase is outside a possible first-order transition.Comment: 6 pages, 4 figures (minor changes

Short-time dynamics of the positional order of the two-dimensional hard disk system

We investigate the positional order of the two-dimensional hard disk model with short-time dynamics and equilibrium simulations. The melting density and the critical exponents z and eta are determined. Our results rule out a phase transition as predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young theory as well as a first-order transition.Comment: 8 pages, 4 figures, minor change

Simulating the Electroweak Phase Transition in the SU(2) Higgs Model

Numerical simulations are performed to study the finite temperature phase transition in the SU(2) Higgs model on the lattice. In the presently investigated range of the Higgs boson mass, below 50 GeV, the phase transition turns out to be of first order and its strength is rapidly decreasing with increasing Higgs boson mass. In order to control the systematic errors, we also perform studies of scaling violations and of finite volume effects.Comment: 46 pages with 16 figures, DESY-94-15

Numerical tests of the electroweak phase transition and thermodynamics of the electroweak plasma

The finite temperature phase transition in the SU(2) Higgs model at a Higgs boson mass $M_H \simeq 34$ GeV is studied in numerical simulations on four-dimensional lattices with time-like extensions up to $L_t=5$. The effects of the finite volume and finite lattice spacing on masses and couplings are studied in detail. The errors due to uncertainties in the critical hopping parameter are estimated. The thermodynamics of the electroweak plasma near the phase transition is investigated by determining the relation between energy density and pressure.Comment: latex2e, 32 pages, 11 figures with epsfig; A few comments and a new table are adde

Critical aging of a ferromagnetic system from a completely ordered state

We adapt the non-linear $\sigma$ model to study the nonequilibrium critical dynamics of O(n) symmetric ferromagnetic system. Using the renormalization group analysis in $d=2+\epsilon$ dimensions we investigate the pure relaxation of the system starting from a completely ordered state. We find that the average magnetization obeys the long-time scaling behavior almost immediately after the system starts to evolve while the correlation and response functions demonstrate scaling behavior which is typical for aging phenomena. The corresponding fluctuation-dissipation ratio is computed to first order in $\epsilon$ and the relation between transverse and longitudinal fluctuations is discussed.Comment: 5 pages, revtex

Identification of the critical temperature from non-equilibrium time-dependent quantities

We present a new procedure able to identify and measure the critical temperature. This method is based on the divergence of the relaxation time approaching the critical point in quenches from infinite temperature. We introduce a dimensionless quantity that turns out to be time-independent at the critical temperature. The procedure does not need equilibration and allows for a relatively fast identification of the critical temperature. The method is first tested in the ferromagnetic Ising model and then applied to the one-dimensional Ising spin glass with power-law interactions. Here we always find a finite critical temperature also in presence of a uniform external field, in agreement with the mean-field picture for the low temperature phase of spin glasses.Comment: 6 pages, 10 figure

Defect fugacity, Spinwave Stiffness and T_c of the 2-d Planar Rotor Model

We obtain precise values for the fugacities of vortices in the 2-d planar rotor model from Monte Carlo simulations in the sector with {\em no} vortices. The bare spinwave stiffness is also calculated and shown to have significant anharmonicity. Using these as inputs in the KT recursion relations, we predict the temperature T_c = 0.925, using linearised equations, and $T_c = 0.899 \pm >.005$ using next higher order corrections, at which vortex unbinding commences in the unconstrained system. The latter value, being in excellent agreement with all recent determinations of T_c, demonstrates that our method 1) constitutes a stringent measure of the relevance of higher order terms in KT theory and 2) can be used to obtain transition temperatures in similar systems with modest computational effort.Comment: 7 pages, 4 figure

População de plantas de soja no sistema de semeadura direta para o Centro-Sul do Estado do Paraná.

bitstream/item/53984/1/47.pd

Numerical simulations of a two-dimensional lattice grain boundary model

We present detailed Monte Carlo results for a two-dimensional grain boundary model on a lattice. The effective Hamiltonian of the system results from the microscopic interaction of grains with orientations described by spins of unit length, and leads to a nearest-neighbour interaction proportional to the absolute value of the angle between the grains. Our analysis of the correlation length xi and susceptibility chi in the high-temperature phase favour a Kosterlitz-Thouless-like (KT) singularity over a second-order phase transition. Unconstrained KT fits of chi and xi confirm the predicted value for the critical exponent nu, while the values of eta deviate from the theoretical prediction. Additionally we apply finite-size scaling theory and investigate the question of multiplicative logarithmic corrections to a KT transition. As for the critical exponents our results are similar to data obtained from the XY model, so that both models probably lie in the same universality class.Comment: 13 pages, Latex, 7 figures, to appear in Physica

Electroweak phase transition by four dimensional simulations

The finite temperature phase transition in the SU(2)-Higgs model at a Higgs boson mass $M_H \simeq 35$ GeV is studied in numerical simulations on four dimensional lattices with time-like extensions up to $L_t=5$. $T_c/M_H$ is extrapolated to the continuum limit and a comparison with the perturbative prediction is made. A one-loop calculation to the coupling anisotropies of the SU(2)-Higgs model on lattices with asymmetric lattice spacings is presented. Our numerical simulations show that the above perturbative result is applicable in the phenomenologically interesting parameter region.Comment: 3 pages, Latex, 3 figures, Talk presented at LATTICE96(electroweak) by Z. Fodo