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:

$\mathcal{H}=-\Lambda\sum_i c_i -\varepsilon\sum_{<i,j>}c_i c_j$

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.

  • 2
    $\begingroup$ You want an explicit expression for the entropy of the 2d Ising model as a function of $h$? None is known. The model has only been solved in the absence of a magnetic field. $\endgroup$ – Yvan Velenik Aug 4 at 11:30

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.

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