# Cluster Approximation for the Two-Dimensional Ising Model

1. Nov 6, 2017

### MathematicalPhysicist

1. The problem statement, all variables and given/known data
In the attachments there is the question and its solution, it's problem 3.5.

2. Relevant equations

3. The attempt at a solution
My question is how did they get the dimensionless Hamiltonian in both cases, and how did they explicitly calculated $m$ in both cases?

I assume it's with $m = \frac{\sum_{\sigma_i}\sigma_i e^{-\beta H}}{\sum e^{-\beta H}}$, but I really don't see how to get to the same terms as in the solution.