arXiv subjects

L. Schuelke

Publications and source records attributed to L. Schuelke.

At least 19 recordsLinked to original sources

arXiv2001

Critical dynamics and universality of the random-bond Potts ferromagnet with tri-distributed quenched disorders

Critical behavior in short-time dynamics is investigated by a Monte Carlo study for the random-bond Potts ferromagnet with a trinary distribution of quenched disorders on two-dimensional triangular lattices. The dynamic scaling is verified and applied to estimate critical exponents $θ$, $z$ and $β/ν$ for several realizations of the trinary distribution. Our critical scaling analysis strongly indicates that the bond randomness influences the critical universality.

cond-mat.stat-mech↗

arXiv2001

Critical exponents of the two-layer Ising model

The symmetric two-layer Ising model (TLIM) is studied by the corner transfer matrix renormalisation group method. The critical points and critical exponents are calculated. It is found that the TLIM belongs to the same universality class as the Ising model. The shift exponent is calculated to be 1.773, which is consistent with the theoretical prediction 1.75 with 1.3% deviation.

cond-mat.soft↗

arXiv2000

Short-time critical dynamics

An introductory review to short-time critical dynamics is given. From the scaling relation valid already in the early stage of the evolution of a system at or near the critical point, one derives power law behaviour for various quantities. By a numerical simulation of the system one can measure the critical exponents and, by searching for the best power law behaviour, one can determine the critical point. Critical slowing down as well as finite size corrections are nearly absent, since the correlation length is still small for times far before equilibrium is reached. By measuring the (pseudo) critical points it is also possible to distinguish (weak) first-order from second-order phase transitions.

hep-lat↗

arXiv2000

The short-time critical behaviour of the Ginzburg-Landau model with long-range interaction

The renormalisation group approach is applied to the study of the short-time critical behaviour of the $d$-dimensional Ginzburg-Landau model with long-range interaction of the form $p^σ s_{p}s_{-p}$ in momentum space. Firstly the system is quenched from a high temperature to the critical temperature and then relaxes to equilibrium within the model A dynamics. The asymptotic scaling laws and the initial slip exponents $θ^{\prime}$ and $θ$ of the order parameter and the response function respectively, are calculated to the second order in $ε=2σ-d$.

cond-mat.soft↗

arXiv2000

Dynamic Approach to Weak First Order Phase Transitions

A short-time dynamic approach to weak first order phase transitions is proposed. Taking the 2-dimensional Potts models as examples, from short-time behaviour of non-equilibrium relaxational processes starting from high temperature and zero temperature states,x pseudo critical points K^{*} and K^{**} are determined. A clear difference of the values for K^{*} and K^{**} distinguishes a weak first order transition from a second order one. At the pseudo critical points, pseudo critical exponents can be estimated.

cond-mat.soft↗

arXiv1999

The Critical Exponent $θ'$ in Spin Glasses

Short-time dynamic scaling behavior of the 3D $\pm J$ Ising spin glass is studied by Monte Carlo methods. Starting the replicas with independent initial configurations with a small pseudo magnetization, the dynamic evolution of the overlap q(t) between two replicas is measured. The initial increase of the overlap q(t) is observed and the corresponding exponent $θ'$ is obtained. From the scaling relation $λ=d/z-θ'$, the dynamic exponent z is estimated.

cond-mat.stat-mech↗

arXiv1998

Short-time Dynamic Behaviour of Critical XY Systems

Using Monte Carlo methods, the short-time dynamic scaling behaviour of two-dimensional critical XY systems is investigated. Our results for the XY model show that there exists universal scaling behaviour already in the short-time regime, but the values of the dynamic exponent $z$ differ for different initial conditions. For the fully frustrated XY model, power law scaling behaviour is also observed in the short-time regime. However, a violation of the standard scaling relation between the exponents is detected.

cond-mat.stat-mech↗

arXiv1998

Short-time Critical Dynamics of the 3-Dimensional Ising Model

Comprehensive Monte Carlo simulations of the short-time dynamic behaviour are reported for the three-dimensional Ising model at criticality. Besides the exponent $θ$ of the critical initial increase and the dynamic exponent $z$, the static critical exponents $ν$ and $β$ as well as the critical temperature are determined from the power-law scaling behaviour of observables at the beginning of the time evolution. States of very high temperature as well as of zero temperature are used as initial states for the simulations.

cond-mat.stat-mech↗

arXiv1998

Dynamic Monte Carlo Study of the Two-Dimensional Quantum XY Model

We present a dynamic Monte Carlo study of the Kosterlitz-Thouless phase transition for the spin-1/2 quantum XY model in two dimensions. The short-time dynamic scaling behaviour is found and the dynamical exponent $θ$, $z$ and the static exponent $η$ are determined at the transition temperature.

cond-mat.soft↗

arXiv1998

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 $θ$, z, $β$ and $ν$.

cond-mat.soft↗

arXiv1997

Monte Carlo Measurement of the Global Persistence Exponent

The scaling behaviour of the persistence probability in the critical dynamics is investigated with both the heat-bath and the Metropolis algorithm for the two-dimensional Ising model and Potts model. Special attention is drawn to the dependence on the initial magnetization. The global persistence exponent is measured. Universality is confirmed.

cond-mat.soft↗

arXiv1997

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 $θ$ vary along the critical line. Another dynamical exponent $z$ is also obtained in the process.

cond-mat↗

arXiv1997

Monte Carlo Simulation of the Short-time Behaviour of the Dynamic XY Model

Dynamic relaxation of the XY model quenched from a high temperature state to the critical temperature or below is investigated with Monte Carlo methods. When a non-zero initial magnetization is given, in the short-time regime of the dynamic evolution the critical initial increase of the magnetization is observed. The dynamic exponent $θ$ is directly determined. The results show that the exponent $θ$ varies with respect to the temperature. Furthermore, it is demonstrated that this initial increase of the magnetization is universal, i.e. independent of the microscopic details of the initial configurations and the algorithms.

cond-mat↗

arXiv1997

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 $θ$ and $z$ as well as the static critical exponent $β/ν$ 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.

cond-mat.soft↗

arXiv1997

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 $θ$ is measured for different temperature and with different algorithms.

cond-mat.soft↗

arXiv1996

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 $θ$ as well as the exponents $z$ and $2β/ν$ 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.

cond-mat↗

arXiv1995

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 $β/ (νz)$ and $1/ (νz)$ are determined.

cond-mat↗

arXiv1995

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 $θ$ as well as exponent $z$ and $β/ν$ 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.

cond-mat↗