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2D Ising model entropy as a function of external field

Physics Asked by BeastRaban on December 12, 2020

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.

One 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.

Answered by Gec on December 12, 2020

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