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 Wolff's 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 Wolff's 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.

Using high statistic numerical results we investigate the properties of the O(3) nonlinear two-dimensional model. Our main concern is the detection of a hypothetical Kosterlitz-Thouless ͑KT-͒like phase transition which would contradict the asymptotic freedom scenario. Our results do not support such a KT-like phase transition. ͓S0556-2821͑99͒03106-9͔

Thermal properties of the ordered phase of the spin-1/2 isotropic Heisenberg Antiferromagnet on a d-dimensional hypercubical lattice are studied within the fermionic representation when the constraint of a single occupancy condition is taken into account by the method suggested by Popov and Fedotov. Using a saddle point approximation in the path integral approach we discuss not only the leading order but also the fluctuations around the saddle point at one-loop level. The influence of taking into account the single occupancy condition is discussed at all steps.

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.

Within the 1/N expansion of O(N ) nonlinear σ models for d ≤ 4 it is possible to separate consistently the spin-wave and the massive-mode contributions to the scaling part of the free energy near criticality, and to evaluate them to O(1/N ). For critical dimensions d = 2 + 2/n the Abe-Hikami anomaly is recovered, while for d = 2 the removal of the spin-wave term is justified.

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We have simulated (3+1)-dimensional finite temperature Z2 gauge theory by using Metropolis algorithm. We aimed to observe the deconfinement phase transitions by using geometric methods. In order to do so we have proposed two different methods which can be applied to three-dimensional effective spin model consisting of Polyakov loop variables. The first method is based on the studies of cluster structures of each configuration. For each temperature, configurations are obtained from a set of bond probability (P) values. At a certain probability, percolating clusters start to emerge. Unless the probability value coincides with the Coniglio–Klein probability value, the fluctuations are less than the actual fluctuations at the critical point. In this method the task is to identify the probability value which yields the highest peak in the diverging quantities on finite lattices. The second method uses the scaling function based on the surface renormalization, which is of geometric origin. Since this function is a scaling function, the measurements done on different-size lattices yield the same value at the critical point, apart from the correction to scaling terms. The linearization of the scaling function around the critical point yields the critical point and the critical exponents.

In this work we have considered the dynamic scaling relation of the magnetization in order to study the dynamic scaling behavior of 2-and 3-dimensional Ising models. We have used the literature values of the magnetic critical exponents to observe the dynamic finite-size scaling behavior of the time evolution of the magnetization during early stages of the Monte Carlo simulation. In this way we have calculated the dynamic critical exponent Z for 2-and 3-dimensional Ising Models by using the Swendsen-Wang cluster algorithm. We have also presented that this method opens the possibility of calculating z and x 0 separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.