  A two dimensional magnetic particle in the presence of an external magnetic
field is studied. Equilibrium thermodynamical properties are derived by
evaluating analytically the partition function. When the external field is
applied perpendicular to the anisotropy axis the system exhibits a second order
phase transition with order parameter being the magnetization parallel to the
field. In this case the system is isomorph to a mechanical system consisting in
a particle moving without friction in a circle rotating about its vertical
diameter. Contrary to a paramagnetic particle, equilibrium magnetization shows
a maximum at finite temperature. We also show that uniaxial anisotropy in a
system of noninteracting particles can be missinterpreted as a ferromagnetic or
antiferromagnetic coupling among the magnetic particles depending on the angle
between anisotropy axis and magnetic field.

Condensed Matter