A Is Block Spin Still ±1 in Ising Model?

[howl]

When one applies block spin scheme on Ising model, what's the value for block spin? If we set the average value for spin in a block, it should not be ±1 anymore. But if so, is the transfer matrix is still two dimensional?

 

[atyy]

There are several different schemes. For example, one can do it using either decimation or majority rule.
https://ocw.mit.edu/courses/physics...ring-2014/lecture-notes/MIT8_334S14_Lec13.pdf (decimation)
https://arxiv.org/abs/0905.2601 (majority rule)

 

[howl]

There are several different schemes. For example, one can do it using either decimation or majority rule.
https://ocw.mit.edu/courses/physics...ring-2014/lecture-notes/MIT8_334S14_Lec13.pdf (decimation)
https://arxiv.org/abs/0905.2601 (majority rule)

Is the block spin scheme the most popular of them?

 

[atyy]

Is the block spin scheme the most popular of them?

The variant schemes are all forms of "block spin". The original block spin is from Kadanoff https://journals.aps.org/ppf/abstract/10.1103/PhysicsPhysiqueFizika.2.263, but I think nowadays the term refers to all variant schemes in which the underlying idea is the same.