2D Ising model entropy as a function of external field

Question

I am trying to figure out what is the entropy expression as a function of the external field in a 2D Ising model with nearest neighbour interaction.
My Hamiltonian is the following:
$mathcal{H}=-Lambdasum_i c_i -varepsilonsum_{<i,j>}c_i c_j$
where $Lambda$ is given by some function of the external field $h$ and $varepsilon$ is constant.
$c_i in {1,-1}$.
I found a measure of the entropy with respect to the temperature, but not with respect to an external field.
If you have an answer please also direct me to a citeable source.

Gec · Answer

Ising model in the external field has three thermodynamical degrees of freedom. I mean, all extensive quantities, such as entropy and internal energy, are functions of three independent variables, for example, $theta, Lambda, N$. What do you mean when asking about entropy as a function of the external field? The analytical solution for the 2D Ising model in the external field is not known. Hence, it is hardly possible to find $S(theta, Lambda, N)$ for the 2D model.
You can find $S(theta, Lambda, N)$, and probably even $S(E, Lambda, N)$, in 1D model.

2D Ising model entropy as a function of external field

One Answer

Add your own answers!

Ask a Question