Is Block Spin Still ±1 in Ising Model?

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Discussion Overview

The discussion revolves around the application of block spin schemes in the Ising model, specifically questioning the value of block spin and the dimensionality of the transfer matrix. Participants explore different methodologies for implementing block spin, including decimation and majority rule, and consider the popularity and definition of block spin schemes.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions whether the average value of spin in a block leads to a block spin value that is no longer ±1, and how this affects the dimensionality of the transfer matrix.
  • Another participant mentions that there are various schemes for block spin, specifically citing decimation and majority rule as examples.
  • A later reply reiterates the existence of different schemes and asks if the block spin scheme is the most popular among them.
  • Further, a participant notes that while the original block spin concept comes from Kadanoff, the term now encompasses various schemes that share the same underlying idea.

Areas of Agreement / Disagreement

Participants express differing views on the value of block spin and the implications for the transfer matrix, indicating that multiple competing perspectives remain on the topic.

Contextual Notes

The discussion does not resolve the assumptions regarding the average spin value in blocks or the definitions of block spin schemes, leaving these aspects open for further exploration.

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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?
 
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