The magnetism and conductance of two-dimensional Heisenberg spin lattices are investigated by using Monte Carlo simulations to qualitatively understand a fascinating magnetoresistance effect observed in magnetic materials and their artificial multilayers. Various magnetic profiles, including a pure ferromagnetic, a pure antiferromagnetic, two phase com-petitive cases, and an artificial sandwich junction, are simulated, and their conductances are calculated based on an extended resistor-network model. Magnetoresistance is observed in some lattices, which is prominent when the system is near phase boundaries. Compared with real manganites, the absence of colossal magnetoresistance in our simulation implies the es- sential role of charge ordered phase which is not included in our pure spin model. However, our model provides an intuitive understanding of the spin-dependent conductance in large scale.
