Within the tight binding method, we study the second order phase transitions in magnetic thin films as a function of the exchange integral J. The transitions from non-magnetic to in-plane antiferromagnetic state which are of second order are analysed in terms of the possible mathematical behaviour. It is shown that such transitions obey a power law rather than an exponential law. No remarkable variation of the corresponding critical exponents ( = 1/2) has been found with the d-band filling, the reduced (...) symmetry, the lattice parameter and the coordination number. (shrink)