The ionic Hubbard model is one of the most important models in solid state physics,that study of its phase diagram has been interesting for researchers. But checking this model because of presence of fermionic creation and annihilation operators, is difficult. So we go through an easier Monte Carlo method we study this model for one and two dimentional squre lattice for nonezero temperature at half filling. Spesific heat for 2,4 and 6 site chains obtained analitically and are compared with Monte Carlo code results. After confirmation of Monte Carlo code, we proceed with calculations in bigger sizes. We also describe transfer matrix method and obtained results from this method in thermodynamic limit are compared with Monte Carlo results, that show a good agreement. Simulation of this problem gives physical quantities such as specific heat and ionicity for one dimentional problem showes band insulator-metalic-Mott insulator phase transition at zero temprature, while phase transition was not observerd at finite temprature. But this calculation for two dimentional problem show lambda phase transition. Our results for one dimentional problem show that substantial parts of quantum model features are justifiable by our dir=ltr Key Words: phase diagram, Monte Carlo method,phase transition.
