(a) Write down the partition function for a 1-dimensional Ising lattice as a sum over terms describing...

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(a) Write down the partition function for a 1-dimensional Ising lattice as a sum over terms describing all possible spin organizations.

(b) Show that by separating into even and odd numbered spins, it is possible to factor the partition function and relate z(N, K)exactly to z(N/2, K'). Specifically, show that

where K' = ln[cosh(2K)]/2, and f (K) = 2[cosh(2K)]^1/2.

(c) Use these relations to demonstrate that the 1-dimensional Ising lattice does not exhibit a second-order phase transition.

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Modern Classical Physics Optics Fluids Plasmas Elasticity Relativity And Statistical Physics

ISBN: 9780691159027

1st Edition

Authors: Kip S. Thorne, Roger D. Blandford

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Question Posted: Apr 30, 2023 06:17 AM

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(a) Write down the partition function for a 1-dimensional Ising lattice as a sum over terms describing...

Question:

z(N, K) = f(K)N/²z(N/2, K') (5.94)

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ANSWER a The partition function for a 1dimensional Ising lattice can be written as a sum over all possible spin configurations ZNK expK i i i1 Here N ...View the full answer

Modern Classical Physics Optics Fluids Plasmas Elasticity Relativity And Statistical Physics

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