3.19. Starting with expression (13.3.8) for the partition function of a one-dimensional n-vector model, with Ji = n)', s

[answerhappygod]

3 19 Starting With Expression 13 3 8 For The Partition Function Of A One Dimensional N Vector Model With Ji N S 1 (83.89 KiB) Viewed 28 times

3.19. Starting with expression (13.3.8) for the partition function of a one-dimensional n-vector model, with Ji = n)', show that 1 I (4K²+ Lim In Qv (nK) = (4K2+1) - 1 - In n.NNN ) [vak + 2:+1}] = where K = BJ'. Note that, apart from a constant term, this result is exactly the same as for the spherical model; the difference arises from the fact that the present result is normalized to give ON = 1 when K=0. (Hint: Use the asymptotic formulae (for v >> 1) r(v) (27/v)1/2 (u/e) and I. (v2) (27v)-1/2 (2+ +1)-1/4" where n = V(+1) - In[{V(z2 + 1) +1)/2].] 3.20. Show that the low-field susceptibility, xo, of the spherical model at T < Te is given by the asymptotic expression xo = (Nu? /BT) Nm3(T),