Yiğit Gündüç

Renormalization and topological susceptibility on the lattice: SU(2) Yang-Mills theory.

The renormalization functions involved in the determination of the topological susceptibility in the SU(2) lattice gauge theory are extracted by direct measurements, without relying on perturbation theory. The determination exploits the phenomenon of critical slowing down to allow the separation of perturbative and non-perturbative effects. The results are in good agreement with perturbative computations.

Gluon condensation in SU(3) lattice gauge theory

Abstract The gluon condensate of dimension 4 is determined for a gauge SU(3) lattice gauge theory. A critical review of the existing procedures to extract the condensate is presented.

The topological susceptibility of the pure SU(3) Yang-Mills vacuum on the lattice☆

Abstract Using a “field theoretic” approach, we compute the topological susceptibility χ of the pure gauge SU(3) theory on the lattice. We also apply an algorithm of gradual cooling, and use these two approaches as a cross-check on each other. The final value we find for χ confirms results found earlier using an abrupt-cooling algorithm.

The deconfining phase transition and the glueball channels in pure gauge QCD

Abstract We study the exponential decay of the smeared plaquettes, at large distance from a cold source, close to the deconfining phase transition of N t =4 lattice QCD. We compare different lattice size results, and by using finite size scaling arguments we find a critical behavior that is in agreement with a continuous transition.

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.

Maximal entanglement from quantum random walks

The conditions under which entanglement becomes maximal are sought in the general one-dimensional quantum random walk with two walkers. Moreover, a one-dimensional shift operator for the two walkers is introduced and its performance in generating entanglement is analyzed as a function of several free parameters, some of them coming from the shift operator itself and some others from the coin operator. To simplify the investigation an averaged entanglement is defined.

A new computation of the correlation length near the deconfining transition in SU(3)

Abstract We compute the correlation length of an SU(3) gauge system in the neighbourhood of the deconfining phase transition by measuring loop-loop correlation functions. We find values that are linearly divergent with the lattice size at the critical point and fully compatible with our former estimates obtained by using a cold source method. Together with a precise determination of the location of the critical point these results make stronger the evidence for a large ξ at β close to β c .

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.

QUANTUM PHASE TRANSITIONS AND ENTANGLEMENT IN J1–J2 MODEL

We study ground state pairwise entanglement within one-dimensional spin-1/2 antiferromagnetic J1–J2 model with competing interactions. Contrary to some claims we found that frustration does not increase entanglement. Concurrence of nearest and next nearest neighbors are found to show abrupt change at phase transition points. We also show that the concurrence can be used to classify the phase diagram of the model in anisotropy–frustration plane.

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.