Monte Carlo and series expansion investigations of magnetic surfaces

The presence of a free surface leads to an inhomogeneous distribution of the local magnetization and other quantities describing the magnetic state of the system. After a brief outline of a general thermodynamic theory, the mean field treatment is discussed and shown to be inconsistent with a more general scaling theory, even if one uses a temperature-dependent extrapolation length. More reliable information is obtained by numerical techniques such as high temperature series expansions and Monte Carlo calculations, which are applied to Ising and Heisenberg models. These numerical results are shown to be consistent with the scaling theory, but it is also shown that the magnetization of the surface layer m
1
depends strongly on the local conditions (e.g., exchange constant J
s
different from
J
in the bulk). Therefore the observability of the universal asymptotic exponents may be restricted to a very narrow region around the (bulk) critical temperature T
cb
. The case where the surface layer orders at a temperature
T_{cs} > T_{cb}
is also considered. The consequences of the theory for thin magnetic films and small particles are outlined and experimental applications are briefly discussed.