Tensor Renormalization Group Method Study in Z5 Model

This thesis describes the Tensor Renormalization Group (TRG) method used to solve the Z5 model in lattice gauge theory. The TRG method provides exact blocking for the models and is much less expansive in terms of computational costs. Here we consider the Z5 model in two dimensions, we discuss the formulation of the tensor and the process we used to do the TRG blocking, in order to find the phase transition and critical behavior of the model. We give some simple results and plots, and some expectation for further research in the model.