Zhongyang Li - University of Connecticut I will discuss the percolation properties of the critical and non-critical XOR Ising models in the 2D Euclidean plane and in the hyperbolic plane, whose spins are products of the spins of two i.i.d Ising models. This is related to the percolation model on an auxiliary lattice satisfying certain locally constraint. New percolation properties of these models can be obtained with the help of ergodicity and symmetry. Part of this talk is based on joint work with Alexander Holroyd.