  By means of Monte Carlo simulations and a finite-size scaling analysis, we
find a critical line of an n-component Eulerian face-cubic model on the square
lattice and the simple cubic lattice in the region v>1, where v is the bond
weight. The phase transition belongs to the Ising universality class
independent of n. The critical properties of the phase transition can also be
captured by the percolation of the complement of the Eulerian graph.
