  We propose a class of models exhibiting instanton crystal phase. In this
phase, the minimum of the free energy corresponds to a configuration with an
imaginary-time-dependent order parameter in a form of a chain of alternating
instantons and antiinstantons. The resulting characteristic feature of this
state is that the average of the order parameter over the imaginary time
vanishes. In order to study the model in a broad region of parameters of the
model quantitatively, and prove the existence of the instanton crystal phase,
we develop an efficient numerical scheme, suitable for the exact treatment of
the proposed models. In a certain limit, results demonstrating the existence of
the instanton crystal phase are obtained also analytically. The numerical study
of the model shows that there is a phase transition between the instanton
crystal and the state with the imaginary-time-independent order parameter.
