Topics in Statistic Mechanics

Adv. Sta. Phy. Homework 7 Renormalization Group Li,Zimeng PB06203182
(1.1.1)
Adding outfield, we have the effective Hamiltonian
1.2 Momentum Space Gauss Model
Changing it to momentum space by FT method, we have
and , where the range (
)is the first Brillouin zone and a is the lattice constant.
is the volume of
primitive cell and we have
The first term of (1.1.1) is rewritten as
=
where B(k)=K
and
Note that when calculating B(k) only nearest neighbours are considered.