On the unique solvability of the Cauchy problem for the equations of motion of discrete analogs of multidimensional chiral fields taking values on compact symmetric spaces

A class of models in classical statistical mechanics that are the discrete analogs of multidimensional chiral fields taking values on compact symmetric spaces is considered. The existence and uniqueness of a solution to the Cauchy problem with arbitrary initial data are proved for the equations of motion of these models. It follows from this result that for the considered models the dynamics exists on the entire infinitedimensional phase space. It is also shown that the constructed dynamics is the limit of a sequence of finite-dimensional dynamics.