Topics in Statistic Mechanics

Adv. Sta. Phy. Homework 7 Renormalization Group Li,Zimeng PB06203182
Renormalization Group
Edited by Li, Zimeng
Contents:
1. Gauss Model
1.1 Introduction
1.2 Momentum Space Gauss Model
1.3 Renormalization Group in Momentum Space
1.4 Derive the Gaussian fix points and Critical exponents
2. Define RG in the language of Ginzburg-Landau model
2.1 Introduction to Ginzburg-Landau Model
2.2 RG solution on G-L model
3. Derive the new fixed point in d=4- dimensions and the associated critical exponents
4. Explain the Universality by RG
1.Gauss Model
1.1 Introduction
Gauss model is a generalization of Ising model. We extend the domain of
in Ising
model to infinity, and introduce in weighing function
Therefore the partition function changes to ,
where K=
Actually, Z does not vanish only when
, which corresponds to Ising model.
In Gauss model we change the weighing function to the form
to ensure
convergence since the domain has been extended to infinity.
Therefore the partition function
with