91Ó°ÊÓ

Plot $\stackrel{¯}{\mathit{s}}$as a function of kT/$\mathrm{Î\mu }$, as predicted by mean field theory, for a two-dimensional Ising model (with a square lattice).

The average spin alignment is given by:

$\stackrel{¯}{s}=\tanh \left(\mathrm{β}\mathrm{Ï\mu }n\stackrel{¯}{s}\right)$

The number of nearest is given by:

$$\begin{gathered} n=2Inonedimension \\ 4Intwodimensions(squarelattice) \\ 6Inthreedimensions(simplecubiclattice) \\ 8Inthreedimensions(bodycenteredcubiclattice) \\ 12Inthreedimensions(facecenteredcubiclattice) \end{gathered}$$

Consider a two-dimensional lsing model with n = 4, which you can plug into the equation above to get:

$\stackrel{¯}{s}=\tanh \left(4\mathrm{β}\mathrm{Ï\mu }\stackrel{¯}{s}\right)$

Substitute $\mathrm{β}=1/k{T}_c$and $t=k{T}_c/\mathrm{Ï\mu }$

$\stackrel{¯}{s}=\tanh \left(\frac{4\stackrel{¯}{s}}{t}\right)$

First, we must solve this equation numerically because it is difficult to solve. To do so, we simply build a list of t values ranging from O01 to 5.0, and then we create a loop to solve this equation numerically for each value of t. I used Python to achieve this, and the code is shown below.

The graph is: