J0=67.2 K, J1=20.9 K, and J2 = −24.2 K, that we have
employed in our simulations. The given values for the ex-
change constants are the same already used by Weschke
et al.in Ref. 13 to interpret experimental data on
Holmium ﬁlms on the basis of a J1 − J2 model, after
a proper scaling by the numbers of NN and NNN on
neighboring layers of a BCT lattice.
In the following we will denote with n the ﬁlm thick-
ness, i.e. the number of spin layers along the z direction,
and with L×L the number of spins in each layer (i.e., L
is the lattice size along both the x and y directions). In
our simulations thickness values from 1 to 24 were con-
sidered, while the range of lateral sizeL was from 8 to
64. Periodic boundary conditions were applied along x
and y, while free boundaries were obviously taken along
the ﬁlm growth direction z.
Thermal equilibrium was attained by the usual
Metropolis algorithm 19, supplemented by the over-
relaxed technique 20 in order to speed-up the sampling
of the spin conﬁguration space: a typical “Monte Carlo
step” was composed by four Metropolis and four-ﬁve
over-relaxed moves per particle. Such judicious mix of
moves is able both to get faster the thermal equilibrium
and to minimize the correlation “time” between succes-
sive samples, i.e. the undesired eﬀects due to lack of in-