Dynamical mean field approach to phase transitions in the Falicov-Kimball model

Abstract

The Falicov-Kimball model is the simplest model of correlated electrons which shows long range order. The Falicov-Kimball model is exactly solvable in the limit of in finite dimensions through the use of Dynamical Mean Field Theory (DMFT). This thesis reviews the Hubbard model and Falicov-Kimball Model in some detail, and details the DMFT formalism. The DMFT formalism is used to investigate continuous second order phase transitions in Falicov-Kimball model. It is seen that the model shows phase transitions for every non-zero value of the interaction strength.