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I'm using the mean field theory approximation and the Ising Model for magnetization to come up with the following equation:

m(T) = tanh(m(T)/T)

where T is an arbitrary temperature

I'm now trying to plot the left side of the equation (m(T)) and the right side of the equation (tanh(m(T)/T) over a range of x -> [-2,2], y-> [-1.1, 1.1], T -> [0.2,2] in steps of 0,2

Separately I also want to graph the solution m(T) = tanh(m(T)/T) for T -> [0,2] as a continuous function

What syntax would I use?

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  • $\begingroup$ Have a look at FindRoot. $\endgroup$
    – b.gates.you.know.what
    Commented Oct 4, 2020 at 20:31
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    $\begingroup$ Are you trying to do this in Mathematica? Look up ContourPlot. Also, I don't understand how the range of x and y enters into plotting an equation that contains no x or y. $\endgroup$
    – Michael E2
    Commented Oct 4, 2020 at 20:34
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    $\begingroup$ What the relations between x, y, and T $\endgroup$
    – cvgmt
    Commented Oct 5, 2020 at 0:21

1 Answer 1

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Try ( see @MichaelE2 's comment )

 ContourPlot[m == Tanh[m /T], {T, .2, 2}, {m, -1, 1},FrameLabel -> {T, m}, MaxRecursion -> 5]

enter image description here

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