  A well-established numerical technique to study the dynamics of spin systems
in which symmetries and conservation laws play an important role is to
microcanonically integrate their reversible equations of motion, obtaining
thermalization through initial conditions drawn with the canonical
distribution. In order to achieve a more realistic relaxation of the magnetic
energy, numerically expensive methods that explicitly couple the spins to the
underlying lattice are normally employed. Here we introduce a stochastic
conservative thermostat that relaxes the magnetic energy while preserving the
constant of motions, thus turning microcanonical spin dynamics into a
conservative canonical dynamics, without actually simulating the lattice. We
test the thermostat on the Heisenberg antiferromagnet in d=3 and show that the
method reproduces the exact values of the static and dynamic critical
exponents, while in the low-temperature phase it yields the correct spin wave
phenomenology. Finally, we demonstrate that the relaxation coefficient of the
new thermostat is quantitatively connected to the microscopic parameters of the
spin-lattice coupling.
