  We study a class of two-dimensional models of classical hard-core particles
with Vicsek-type "exchange interaction" that aligns the directions of motion of
nearby particles. By extending the Hohenberg-Mermin-Wagner theorem for the
absence of spontaneous magnetization and the McBryan-Spencer bound for
correlation functions, we prove that the models do not spontaneously break the
rotational symmetry in their equilibrium states at any nonzero temperature. We
thus conclude that the mobility of particles alone does not account for the
spontaneous symmetry breaking in Vicsek type models. The origin of the symmetry
breaking must be sought in the absence of detailed balance condition, or,
equivalently, in the nonequilibrium nature.
