FINITE SIZE SCALING BY USING SCALING FUNCTIONS IN TWO-DIMENSIONAL q = 2 AND 7 STATE POTTS MODELS

Demirtürk, Semra; Seferoğlu, Nurgül; Aydın, Meral; Gündüç, Yiğit

doi:10.1142/s0129183101001808

Cited by 3 publications

(5 citation statements)

References 12 publications

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“…The second quantity is the scaling function (F ) based on the surface renormalization. This function is studied in detail for the Ising model [16,17,18] and q-state Potts model [19,20,21]. In order to calculate this function, one considers the direction of the majority of spins of two parallel surfaces which are L/2 distance away from each other.…”

Section: Introductionmentioning

confidence: 99%

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

Gündüç¹,

Dilaver²,

Aydın³

et al. 2005

Computer Physics Communications

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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.

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Section: Introductionmentioning

confidence: 99%

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

Gündüç¹,

Dilaver²,

Aydın³

et al. 2005

Computer Physics Communications

Self Cite

View full text Add to dashboard Cite

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“…The second quantity is the scaling function (F ) based on the surface renormalization. This function is studied in detail for the Ising model [16][17][18] and q-state Potts model [19][20][21]. We propose that the dynamic finite size scaling relation also holds for the scaling functions and the scaling relation can be written similarly to the moments of the magnetization,…”

Section: The Methodsmentioning

confidence: 99%

Dynamic critical index of the Swendsen–Wang algorithm by dynamic finite-size scaling

Dilaver

Gündüç

Aydın

et al. 2006

Computer Physics Communications

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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.

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“…The function F is studied in detail for the Ising Model [18,19,20] and q-state Potts Model [21,22]. In order to calculate this function, one considers the direction of the majority of spins of two parallel surfaces which are L/2 distance away from each other.…”

Section: Model and The Methodsmentioning

confidence: 99%

“…In this work we aim to apply two different techniques to the effective spin system obtained from the finite temperature gauge theory. The success of these techniques are previously tested on spin systems for first-and second-order phase transitions [17,18,19,20,21,22].…”

Section: Introductionmentioning

confidence: 99%

“…The first approach which we will apply to the (3+1)−dimensional finite temperature Ising gauge theory is the method which is based on determining the Coniglio-Kleinlike probability value which produces the largest fluctuations in the 3−dimensional effective spin system consisting of the Polyakov loop variables [17]. The second approach that we want to implement on lattice gauge theories uses the scaling function based on the surface renormalization [18,19,20,21,22]. Both methods can easily be implemented to follow the deconfinement phase transition into finite mass quark region.…”

Section: Introductionmentioning

confidence: 99%

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TWO GEOMETRIC APPROACHES TO STUDY THE DECONFINEMENT PHASE TRANSITION IN (3+1)-DIMENSIONAL Z₂ GAUGE THEORIES

Gündüç

Dilaver

Gündüç

2004

Int. J. Mod. Phys. C

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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.

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FINITE SIZE SCALING BY USING SCALING FUNCTIONS IN TWO-DIMENSIONAL q = 2 AND 7 STATE POTTS MODELS

Cited by 3 publications

References 12 publications

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

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

Dynamic critical index of the Swendsen–Wang algorithm by dynamic finite-size scaling

TWO GEOMETRIC APPROACHES TO STUDY THE DECONFINEMENT PHASE TRANSITION IN (3+1)-DIMENSIONAL Z₂ GAUGE THEORIES

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FINITE SIZE SCALING BY USING SCALING FUNCTIONS IN TWO-DIMENSIONAL q = 2 AND 7 STATE POTTS MODELS

Cited by 3 publications

References 12 publications

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

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

Dynamic critical index of the Swendsen–Wang algorithm by dynamic finite-size scaling

TWO GEOMETRIC APPROACHES TO STUDY THE DECONFINEMENT PHASE TRANSITION IN (3+1)-DIMENSIONAL Z2 GAUGE THEORIES

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TWO GEOMETRIC APPROACHES TO STUDY THE DECONFINEMENT PHASE TRANSITION IN (3+1)-DIMENSIONAL Z₂ GAUGE THEORIES