Question

3. Consider the generalized one-dimensional Ising model with link-dependent interactions J. In other words, we have N spins s, in a chain and energy N-1 SiSi+1 We recover a standard Ising model (with B 0 and open boundary condi tions) if we set JiJN-1-J a) Show that the canonical partition function is Hint: You can do this by induction and carefully comparing the states of the N-spin chain to those of the (N - 1)-spin chain.] b) Show that the expected average of the product of two arbitrary spins, sksk+r), r > 0, is given by orz In the case that J-.JN-1J, this tells us that (sksk+r)- [tanh(BJ)]"

Answer 1

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