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.

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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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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.