Verify this result. Further, show that with this choice for ∆H, the first-order perturbation ap-proximation for the free energy corresponds to ϱ= ϱ NF , and that k B T In ϱMF is actually an upper...

Verify this result. Further, show that with this choice for ∆H, the first-order perturbation ap-proximation for the free energy corresponds to
ϱ= ϱ
_NF
, and that k_B
T
In ϱMF is actually an upper bound to the exact free energy.

Q13

Start with K =10 which is large enough to approximate
ϱ (10, N) ≈
ϱ (K → ∞, N) =2, exp(NK)- that is, g (10) ≈10. Apply the RG equation (a) and (b) and generate a table like that on p. 141 but which progresses from large K to small K. Show that by applying equations (C) and (d), the errors in the nth iteration are 2^-n
smaller than the error in the initial estimate of g: and show that the errors
grow
exponentially when you apply (a) and (b).