In this paper, we have investigated the critical behavior of the ferro
magnetic Ising model on union jack lattice. The model is equivalent to
the eight-vertex model which can be solved as a free fermion model wi
th the free fermion approximation. The critical exponents have been ob
tained as alpha = alpha' = 0, beta = beta' = 0.125, gamma = gamma' = 0
.875 and delta = delta' = 8.