Complexity Explorer Santa Few Institute

Introduction to Renormalization

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4.1 Fixing a projection: From CA’s to Ising » Quiz Solution

What can happen when you coarse-grain a system and ask how the model renormalizes?

A. the model parameters change

B. you move from one model in the class to another model in the class.

C. the new coarse-grained system can no longer be exactly described by any of the models in the class.

D. any of the above.


Answer: (D). (A) we saw an example of in the case of the Markov Chains (Unit #2). (B) we saw an example of in Israeli and Goldenfeld's work; you could find projections that took you from one model (e.g., Rule 105) to another (e.g., Rule 150). (C) we saw when we took Rule 90 and used the Alice coarse-graining where we did majority vote on groups of three cells; in this latter case, it appeared that no Markovian model, at any time-scale, would work.