  We find by simulation that the interfaces in the exclusive-or (XOR) of two
independent 2D Ising spin configurations at the critical temperature form an
ensemble of loops that have the same distribution as the contour lines of the
Gaussian free field, but with the heights of the contours spaced \sqrt{2} times
as far apart as they are for the conformal loop ensemble CLE_4 or the double
dimer model on the square lattice. For domains with boundary, various natural
boundary conditions for the two Ising models correspond to certain boundary
heights for the Gaussian free field.
