  We study by extensive Monte Carlo (MC) simulations and analytical Green
function (GF) method effects of frustrated surfaces on the properties of thin
films made of stacked triangular layers of atoms bearing Heisenberg spins with
an Ising-like interaction anisotropy. We suppose that the in-plane surface
interaction $J_s$ can be antiferromagnetic or ferromagnetic while all other
interactions are ferromagnetic. We show that the ground-state spin
configuration is non linear when $J_s$ is lower than a critical value $J_s^c$.
The film surfaces are then frustrated. In the frustrated case, there are two
phase transitions related to disorderings of surface and interior layers. There
is a good agreement between MC and GF results. In addition, we show from MC
histogram calculation that the value of the ratio of critical exponents
$\gamma/\nu$ of the observed transitions is deviated from the values of two and
three Ising universality classes. The origin of this deviation is discussed
with general physical arguments.
