  A two dimensional (2D) percolation transition in Fe/W(110) ultrathin magnetic
films occurs when islands in the second atomic layer percolate and resolve a
frustrated magnetic state to produce long-range in-plane ferromagnetic order.
Novel measurements of the magnetic susceptibility $\chi(\theta)$ as the films
are deposited at a constant temperature, allow the long-range percolation
transition to be observed as a sharp peak consistent with a critical phase
transition. The measurements are used to trace the
paramagnetic-to-ferromagnetic phase boundary between the $T=0$ percolation
magnetic transition and the thermal Curie magnetic transition of the undiluted
film. A quantitative comparison to critical scaling theory is made by fitting
the functional form of the phase boundary. The fitted parameters are then used
in theoretical expressions for $\chi(T)$ in the critical region of the
paramagnetic state to provide an excellent, independent representation of the
experimental measurements.
