In this paper, quantum versions of statistical models are constructed. All aspects of the systems can be explicitly solved. It is possible to give magnetic realizations of these models. The most interesting conclusions are: (1) the state for time going to infinity is approached in an oscillatory manner in the quantum case; (2) in both classical and quantum cases, the exact description gives limiting states which remember the initial specifications; and (3) in these models, the time evolution generally cannot be described. even approximately, by a master equation.