  "Swing" effects at the onset of crossover towards two dimensional behavior in
thin Ising films are investigated close to Tc(D) by means of Monte Carlo
calculations. We find that the effect is extremely large for the specific heat
effective critical exponent, in comparison with the "swing" already noted by
Capehart and Fisher for the susceptibility. These effects change considerably
the system's evolution with thickness (D) from two-dimensional to
three-dimensional behavior, forcing the effective exponents to pass near
characteristic Tri Critical Point (TCP) values.
