  Using the Trace Minimization Algorithm, we carried out an exact calculation
of entanglement in a 19-site two-dimensional transverse Ising model. This model
consists of a set of localized spin-1/2 particles in a two dimensional
triangular lattice coupled through exchange interaction J and subject to an
external magnetic field of strength h. We demonstrate, for such a class of
two-dimensional magnetic systems, that entanglement can be controlled and tuned
by varying the parameter $\lambda$ = h/J in the Hamiltonian and by introducing
impurities into the systems. Examining the derivative of the concurrence as a
function of $\lambda$ shows that the system exhibits a quantum phase transition
at about $\lambda_c$ = 3.01, a transition induced by quantum fluctuations at
the absolute zero of temperature.
