The repulsive Lome force between two vortices in high-K superconductors with the vortices aligned along the direction of axial symmeuy was calculated by approximating the numerical intend by a set of polynomials to speed up the computations. Calculations were carried out ta simulate formation of hexagonal vortex lattice fiom a population of 4W initially randomly distributed vortices. Small domains with different alignments of vortices were found at the early stages and a single large domain with hexagonal order aligned with the edges emerged at lhe end. Also, the expansion of a vortex population was simulated and it kept its initial shap while it expanded isotopically outward into a larger area The force exerted on a displaced vortex io an otherwise prfect latlice was calculated and it was found to be aboul the same order of magnitude as the force between two isolated vortices, and about ten times stronger than the force exerted on an extra interstitial vortex.

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The bounds of entanglement on antiferromagnetic (AF) isotropic Heisenberg spin-1/2 chain including dipoledipole interaction (D) were investigated. The Quantum Monte Carlo method based on loop algorithm was employed to calculate the two-spin and single-spin expectation values mediating the lower and upper bounds. It was revealed that D and B z (the applied magnetic field) were pivotal parameters in controlling either entanglement creation/extinction or entanglement enhancement/weakening. Rival regions indicated a revival phenomenon depending on the temperature for various strengths of D which also showed a nonmonotonic behavior under certain Bz identifying critical points. Even if thermal agitations break the stability of strong D entanglement, it remains invariable at very low temperatures.