Markov Semigroups Which Describe the Time Evolution of Some Higher Spin Quantum Models

We consider perturbation of spin′s ferromagnetic Heisenberg models in infinite volume ground state representations. Imaginary time evolution gives rise to a Markov semigroup on a configuration space of the classical spin system. We establish a correspondence of reversible measures for Markov semigroups and ground states of quantum systems on the same dimensional lattice.