Given the standard Ising partition function:
Z(θ,h)=∑xexp{θ∑(i,j)∈Exixj+h∑i∈Vxi},
is there a closed form expression for the lower bound of the free-energy (Pressure) per-site, defined as,
ψ(θ,h)=limn→∞log(Z(θ,h))n.
My hunch is that is 2θ+h based on taking limits of an approximation suggested in this article
Any ideas on its suitability as a lower bound?
This post imported from StackExchange Physics at 2014-06-21 09:02 (UCT), posted by SE-user user48476