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# 9: Renormalization

• 9.1: The Program of Renormalization
• 9.2: Real Space Renormalization
There are two different classes of renormalization. One class, called real space renormalization group (RSRG), eliminates local lattice-based degrees of freedom at each step in the RG process. The second class, called momentum space renormalization group (MSRG), is implemented by systematically lowering the cutoff Λ in the wavevector integrals. It turns out that the RSRG process, for reasons we shall see, is uncontrolled, and for ‘professional’ results one resorts to MSRG.
• 9.3: Block Spin Transformation
Spin blocking refers to a process in which we replace a group of spins by a single spin whose direction is determined by ‘majority rule’. That is, if most of the spins in the group are up, then the block spin is said to be up; if most spins are down, then the block spin is down.
• 9.4: Scaling Variables
• 9.5: RSRG on Hierarchical Lattices The
• 9.S: Summary

Thumbnail: RG flow for the Ising model with nearest and nearest neighbor interactions.