Thermodynamics of the Two-Dimensional Ising Model with Regularly Disposed Frustrations

A numerically exact method is presented to calculate the thermodynamic quantities of twodimensional Ising models with complicated but regularly disposed frustrations. The method is used to study several kinds of frustration models. The layered frustration model is studied in detail to reveal the effect of frustrations on phase transition. It is shown that (1) single layers of frustration prevent the correlation from propagating over the entire region resulting no global ordering at finite temperatures, whereas (2) even layers of frustration help the correlation growing to the global ordering. In the latter case the critical behavior is characterized by the liogarithmic singularity. The difference of frustration arrangements has no effect on the transition temperature but is related strongly with the critical amplitudes.