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

Hohenberg-Mermin-Wagner type theorems for equilibrium models of flocking