On the Segregation Phenomenon in Complex Langevin Simulation

In the numerical simulation of certain field theoretical models, the complex Langevin simulation has been believed to fail due to the violation of ergodicity. We give a detailed analysis of this problem based on a toy model with one degree of freedom ($S=-\beta\cos\theta$). We find that the failure is not due to the defect of complex Langevin simulation itself, but rather to the way how one treats the singularity appearing in the drift force. An effective algorithm is proposed by which one can simulate the ${1/\beta}$ behaviour of the expectation value $$ in the small $\beta$ limit.Comment: (20 pages + 8 figures on request). Siegen Si-93-8, Tokuyama TKYM-93-

Determination of the Critical Point and Exponents from short-time Dynamics

The dynamic process for the two dimensional three state Potts model in the critical domain is simulated by the Monte Carlo method. It is shown that the critical point can rigorously be located from the universal short-time behaviour. This makes it possible to investigate critical dynamics independently of the equilibrium state. From the power law behaviour of the magnetization the exponents $\beta / (\nu z)$ and $1/ (\nu z)$ are determined.Comment: 6 pages, 4 figure

Universality and Scaling in Short-time Critical Dynamics

Numerically we simulate the short-time behaviour of the critical dynamics for the two dimensional Ising model and Potts model with an initial state of very high temperature and small magnetization. Critical initial increase of the magnetization is observed. The new dynamic critical exponent $\theta$ as well as the exponents $z$ and $2\beta/\nu$ are determined from the power law behaviour of the magnetization, auto-correlation and the second moment. Furthermore the calculation has been carried out with both Heat-bath and Metropolis algorithms. All the results are consistent and therefore universality and scaling are confirmed.Comment: 14 pages, 14 figure

Universal Short-time Behaviour of the Dynamic Fully Frustrated XY Model

With Monte Carlo methods we investigate the dynamic relaxation of the fully frustrated XY model in two dimensions below or at the Kosterlitz-Thouless phase transition temperature. Special attention is drawn to the sublattice structure of the dynamic evolution. Short-time scaling behaviour is found and universality is confirmed. The critical exponent $\theta$ is measured for different temperature and with different algorithms.Comment: 18 pages, LaTeX, 8 ps-figure

Dynamic SU(2) Lattice Gauge Theory at Finite Temperature

The dynamic relaxation process for the (2+1)--dimensional SU(2) lattice gauge theory at critical temperature is investigated with Monte Carlo methods. The critical initial increase of the Polyakov loop is observed. The dynamic exponents $\theta$ and $z$ as well as the static critical exponent $\beta/\nu$ are determined from the power law behaviour of the Polyakov loop, the auto-correlation and the second moment at the early stage of the time evolution. The results are well consistent and universal short-time scaling behaviour of the dynamic system is confirmed. The values of the exponents show that the dynamic SU(2) lattice gauge theory is in the same dynamic universality class as the dynamic Ising model.Comment: 10 pages with 2 figure

The short-time behaviour of a kinetic Ashkin-Teller model on the critical line

We simulate the kinetic Ashkin-Teller model with both ordered and disordered initial states, evolving in contact with a heat-bath at the critical temperature. The power law scaling behaviour for the magnetic order and electric order are observed in the early time stage. The values of the critical exponent $\theta$ vary along the critical line. Another dynamical exponent $z$ is also obtained in the process.Comment: 14 pages LaTeX with 4 figures in postscrip

The short-time Dynamics of the Critical Potts Model

The universal behaviour of the short-time dynamics of the three state Potts model in two dimensions at criticality is investigated with Monte Carlo methods. The initial increase of the order is observed. The new dynamic exponent $\theta$ as well as exponent $z$ and $\beta/\nu$ are determined. The measurements are carried out in the very beginning of the time evolution. The spatial correlation length is found to be very short compared with the lattice size.Comment: 6 pages, 3 figure

Eiszeitliche Ablagerungen in Hochlagen des Süntels (Süd-Hannover) und seinen Karstschlotten

Aus dem Karstgebiet des Riesenberges im Süntel werden hochgelegene kies- und steinführende Ablagerungen verschiedenen Alters beschrieben. Außer kiesführenden Höhlensedimenten präglazialen Alters treten kiesführende Ablagerungen auf, die eiszeitlich entstanden sind. Während die Kies- und Steinanteile der präglazialen Ablagerungen aus lokalen (Kalkstein des Malm) und z. T. ortsfremden Komponenten (Sandstein des Wealden) bestehen, enthalten die jüngeren Ablagerungen zusätzlich Kiesanteile aus nordisch-skandinavischen Gesteinen sowie resedimentierten Weserkies. Die eiszeitlichen Ablagerungen wurden im Kammbereich sowie in Karsthöhlen abgelagert.Gravel deposits positioned in high altitude areas of Süntel Mountains are described from the carst area of Riesenberg. Not only cave gravel of pre-glacial age, but also those of glacial age occur. While the pre-glacial deposits comprise local, but xenotopic components, the younger ones display also material of northern derivation as well as reworked gravels from the Weser-River. The sediments were deposited both in caves and at summit region of the Süntel Mountains. Conditions of deposition and age relation to the glaciations are discussed

Dynamic Approach to the Fully Frustrated XY Model

Using Monte Carlo simulations, we systematically investigate the non-equilibrium dynamics of the chiral degree of freedom in the two-dimensional fully frustrated XY model. The critical initial increase of the staggered chiral magnetization is observed. By means of the short-time dynamics approach, we estimate the second order phase transition temperature $T_{c}$ and all the dynamic and static critical exponents $\theta$, z, $\beta$ and $\nu$.Comment: 5 pages with 6 figures include