Physics Asked on November 28, 2020
I am struggling to understand how they have ploted some functions regarding the Ising model in the mean field approximation (Curie-Weiss model) in my lecture notes
For more details,you can see them here
https://drive.google.com/file/d/1TPFsNwuuVA5uLDNyZkJRyaFdIorUC9nn/view?usp=sharing
The hamiltonian of the model is
The magnetic susceptibility as computed from the combinatorial approach to the Curie-Weiss model yields the following expression:
where $m$ is the magnetization density which varies in $[-1,1]$ and J is the hamiltonian’s energy coupling term.
and the following plot is presented:
I am trying to plot this myself. I have to express $chi_T$ as a function of T/J. They are considering $beta=1/T$, so:
$$chi_T= frac{1}{T}(1-tanh^2[frac{h+Jm}{T})])$$
to try to make the T/J ratio show up, I do:
$$chi_T= frac{1}{J}frac{1}{T/J}(1-tanh^2[frac{h+Jm}{JT/J})])$$ and calling r=T/J:
$$chi_T(r)= Jfrac{1}{r}(1-tanh^2[frac{h+Jm}{Jr})])$$
They have plotted this relation for $ h=0$ and $h=0.1$. The problem is that I don’t know the values of $m $and $J$, and no mention of them is made in the document. Am I supposed to assign random values? If so, how do I assign coherent values?
Clueless as to what values to assign, I assigned for h=0 case: J=1, and m=1 ,and I got:
But I am not getting the peak at $T/J=r=1$ and its corresponding value $chi_T=1$ which is an important feature of the model
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