also as x − y planes, while z will be taken parallel to c.
For n > 16, n being the number of spin layers in the ﬁlm,
a correct bulk limit is reached, while for lower n the ﬁlm
properties are clearly aﬀected by the strong competition
among the helical pitch and the surface eﬀects, which in-
volve the majority of the spin layers. In the thickness
rangen = 9 − 16, i.e. right for thickness values com-
parable with the helical pitch, three diﬀerent magnetic
phases emerged, with the high-temperature, disordered,
paramagnetic phase and the low-temperature, long-range
ordered one separated by an intriguing, intermediate-
temperature block phase, where outer ordered layers co-
exist with some inner disordered ones, the phase tran-
sition of the latter eventually displaying the signatures
of a Kosterlitz-Thouless one. Finally, forn ≤ 7 the ﬁlm
collapses once and for all to a quasi-collinear order.
The complex phase diagram unveiled by such MC sim-
ulations awaken however a further intriguing question:
to what extent the observed behavior may be considered
a simple consequence of the competition between helical
order and surface eﬀects? I.e., is it just a matter of hav-
ing such a competition or does the range of interactions
also play a relevant role? Indeed, when the range of the
interactions is large enough we have a greater number of
planes which can be thought of as ”surface planes”, i.e.
for which the number of interacting neighbors are sig-
niﬁcantly reduced with respect to the bulk layers; there-
fore, we expect that the larger the interaction range, the
stronger should be the surface eﬀects. But, at the same
time, the same modulation of the magnetic order can