Meral Aydin

STUDY OF CLUSTER FLUCTUATIONS IN THE TWO-DIMENSIONAL Q-STATE POTTS MODEL

The two-dimensional Potts Model with 2 to 10 states is studied using a cluster algorithm to calculate fluctuations in cluster size as well as commonly used quantities like equilibrium averages and the histograms for energy and the order parameter. Results provide information about the variation of cluster sizes depending on the temperature and the number of states. They also give evidence for first-order transition when energy and the order parameter related measurables are inconclusive on small size lattices.

A study of dynamic finite size scaling behavior of the scaling functions: calculation of dynamic critical index of Wolff algorithm

Abstract In this work we have studied the dynamic scaling behavior of two scaling functions and we have shown that scaling functions obey the dynamic finite size scaling rules. Dynamic finite size scaling of scaling functions opens possibilities for a wide range of applications. As an application we have calculated the dynamic critical exponent ( z ) of Wolffs cluster algorithm for 2-, 3- and 4-dimensional Ising models. Configurations with vanishing initial magnetization are chosen in order to avoid complications due to initial magnetization. The observed dynamic finite size scaling behavior during early stages of the Monte Carlo simulation yields z for Wolffs cluster algorithm for 2-, 3- and 4-dimensional Ising models with vanishing values which are consistent with the values obtained from the autocorrelations. Especially, the vanishing dynamic critical exponent we obtained for d = 3 implies that the Wolff algorithm is more efficient in eliminating critical slowing down in Monte Carlo simulations than previously reported.

CLUSTER DISTRIBUTIONS IN TWO-DIMENSIONAL Q-STATE POTTS MODEL

Abstract Two-dimensional Potts model with q = 2–10 states is studied using a cluster algorithm to investigate the distributions of cluster sizes. Results concerning the distribution of clusters depending on the temperature and the number of states give supporting evidence for the order of the transition when energy and the order parameter related measurables are inconclusive on small size lattices.

TWO-DIMENSIONAL SEVEN-STATE POTTS MODEL UNDER EXTERNAL MAGNETIC FIELD

The two-dimensional Potts model with seven states under external field is studied using a cluster algorithm. Cluster size distribution and the fluctuations in the average cluster size provide helpful information on the order of phase transitions.

Short-time dynamics of cluster growth in the Potts model

The two- and three-dimensional q-state Potts model is simulated by a cluster algorithm and the relaxation dynamics of average cluster size and the order parameter during initial thermalization are studied. The dependence of these quantities on the lattice size and q in the early stages of Monte Carlo iterations reveals valuable information on the nature of the phase transition occurring in the system. From the initial thermalization data of the 2D 7-state Potts model, surface tension is also calculated. The value is in good agreement with the exact result.

Scaling of cluster fluctuations in two-dimensional q=5 and 7 state Potts models

The scaling behavior of fluctuations in cluster size is studied in q=5 and 7 state Potts models. This quantity exhibits scaling behavior on small lattices where the scaling of local operators like energy fluctuations and Binder cumulant cannot be expected.

Dynamics of clusters in the two-dimensional Potts model

Dynamical behavior of clusters during relaxation is studied in the two-dimensional Potts model using a cluster algorithm. Average cluster size and cluster formation velocity are calculated on two different lattice sizes for different number of states during initial stages of the Monte Carlo simulation. Dependence of these quantities on the order of the transition provides an efficient method to study nature of the phase transitions occurring in similar models.

A NEW APPROACH TO DYNAMIC FINITE-SIZE SCALING

In this work we have considered the Taylor series expansion of the dynamic scaling relation of the magnetization with respect to small initial magnetization values in order to study the dynamic scaling behavior of two- and three-dimensional Ising models. We have used the literature values of the critical exponents and of the new dynamic exponent x0 to observe the dynamic finite-size scaling behavior of the time evolution of the magnetization during early stages of the Monte Carlo simulation. For the three-dimensional Ising model we have also presented that this method opens the possibility of calculating z and x0 separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.

Cluster Study in the Three-Dimensional 3-State Potts Model

The three-dimensional 3-state Potts model has been investigated by examining the average cluster size distributions. Cluster distributions give evidence for the weak first-order nature of the transition for lattice sizes as small as 163, where the energy histogram method fails to exhibit the true nature of the transition.