Topics in Statistic Mechanics

Adv. Sta. Phy. Homework 7 Renormalization Group Li,Zimeng PB06203182
In the coarse grain transformation, the real length is increased to b times large, which
corresponds to a b times decrease in momentum space.So we need to integrate out the
momentum length which is larger than ,or the short wave section (since k= ),
is the lattice constant in momentum space.
We divide k into two parts: (define l as the length of spin block or coarse grain, l is just
the rescale factor b above)
Long wave part
Short wave part
We also divide spin into two parts:
means short wave,thus
in (1.2.2) is
, L means long wave and S
Therefore (1.2.2) can be rewritten as +
And Z=