Question

PHY3703 Oct/Nov 2018 4 The spin-spin correlation function for the one-dimensional Ising model is defined as G (r) 3Sr-3S where r s the separation between the two spins in unuts of the lattice constant, and the averages are to be taken over all microstates Consider an Ising chain of N=3 spins with free boundary conditions in equlibrium with a heat bath at temperature T and in zero magnetic field (a) Enumerate all the microsates of this chain (8 (9) (b) Calculate the expressions for G (1) and G (2), for k 1 (c) Explain the asymptotic behaviour of the expressions obtained imiting (b) for the (3 0 and T cases T 20

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Answer 1

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b) guual pin-Apin Co-rrtlatu m (ken Gn S, S491 G & Hominonim anknou tndion S,S3 e-fah d-Led2 S 3 26 12 2+ 2 e-f 3 2 2 et -2p Scanned with CamScanner

Si,,S3 e-f(+S,) 2P 2 2 S e-f (sS5) S,SS2 e-f(sas) ,S e-f(i+Sa) S3 3et) 2 +2 S, S,S3 e-(S+s) Si, S2 e-fe-f e- of 2e-+) Scanned with CS CamScanner

G) S,52 f- (e-afli) e-1P 6e-f 21 e-1P Now, Si S e - S,S e-(2s.) S2 re-f GC) 2 - -42) csSca CamScanner with