Entanglement in One-Dimensional Open Chains of Spins 1/2 with XY-Hamiltonian

We investigate entanglement of spin pairs in a one-dimension open chain of spins coupled by the dipole-dipole interactions (DDI) in the equilibrium state in the external magnetic field. We suggest a method of calculation of the reduced density matrix. Concurrence, the quantitative measure of the entanglement, is estimated with Wootter's criteria. Analytical and numerical methods are used in order to investigate the influence of the temperature, chain's length, distance between the spins and their distance from the chain's ends on their entanglement.