Complexity Explorer Santa Fe Institute

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Introduction to Renormalization

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4.5 Finding Fixed Points » Quiz Solution

What's the renormalization group flow for the Ising model in our coarse-grained approximation?

A. a 1-dimensional model space flows to a single point

B. a 1-dimensional model space flows to one of two distinct points

C. a 1-dimensional model space flows to one of three distinct points

D. none of the above

 

Answer: (C). When beta is below a critical value, repeated renormalizations drive you to zero -- a decoupled state. When it's above a critical value, beta gets extremely large. When it's precisely at the critical value, it stays fixed at a finite (non-zero) value.