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Introduction
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Coarse graining Alice and Dinah
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Coarse graining part I - Clustering algorithms
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Coarse graining part II - Entropy
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Markov Chains
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Mathematics of coarse grained Markov chains
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Mathematics of Coarse grained Markov Chains: The General Case
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A puzzle: origin of the slippy counter
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Where we are so far
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Cellular Automata: Introduction
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Israeli and Goldenfeld; projection and commuting diagrams
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Networks of Renormalization
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Fixing a projection: From CA’s to Ising
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Introduction to the Ising Model
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Coarse-graining the Lattice
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Inducing Quartets & Commutation Failure
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Finding Fixed Points
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Ising Model Simulations
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Poking the Creature: An Introduction to Group Theory
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Irreversible Computations, Forgetful Computers and the Krohn-Rhodes Theorem
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From Quantum Electrodynamics to Plasma Physics
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The Thermal Physics of Plasma
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How does a particle move the plasma?
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Charge Renormalization and Feedback
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Conclusion: Keeping the things that matter
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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.