# 2D Ising Model (analytical expressions)

## Main Question or Discussion Point

Hi all,

I am doing a program to simulate the 2D Ising Model under the metropolis algorithm. In order to check my results I would like to compare them with the analytical expressions for the mean energy, magnetization, specific heat and magnetic susceptibility.

I already found the expressions for the mean energy, magnetization and specific heat. However, when I plot the expression for the mean energy the result does not look right. I used the one in Huang's book. Concerning the magnetic susceptibility, I couldn't find any analytical expression...

Anyone could give me some help? Thanks.

Best regards!

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If you have the expression for the magnetisation for a given applied field you should be able to go from there to the susceptibility...

Hi,

Thank you for your reply. I am only interested in the case with B=0.

The expression for the magnetization is $M=[1-\sinh^{-4}(2/k_B T)]^{1/8}$.

The susceptibility is obtained from $\chi = \frac{<M^2>- <M>^2}{k_B T}$.

But I don't know the analytical expression for $\chi$...