Monte Carlo and self-consistent feynman diagram studies of magnetic and correlated electron models

A Metropolis-Type Dynamics and the Monte Carlo Damage Spreading technique are proposed to study Ising,mixed-spin Ising,and Blume-Capel models on the 2- dimensional square lattice.For the mixed spin Ising model,our results strongly suggest that this spin model may have a tricritical point at .nite temperature;For S =1 and 2 integer spin Blume-Capel models,our results suggest there exists one multi-critical point along the order-disorder transition line.For S =3/2 and 5/2 half- integer spin Blume-Capel models,our results show that this multi-critical behavior does not exist. The Self-Consistent High-Order Feynman Diagram Expansion Technique is intro- duced and then employed to study two correlated electron models:the Hubbard Model (HBM)and the Anderson Impurity Model (AIM)with maximum expansion order n =3.The basic idea of Monte Carlo Summation technique combined with the Self-Consistent Feynman Diagram Expansion,the initial results,and proposed future work on this topic are also presented.