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Are you asking for a plot of $z(d)$ and $w(d)$? Wolfram Alpha might not like the long query, but Mathematica simplifies your number/letter soup just fine: $$w(d)=-\sqrt{3}\frac{ d^2 (x+2 y-1)-2 d \left(x (2 y-1)+y^2\right)+x (4 y-3)-2 y^2+6 y-3}{d^2-2 d y+4 y^2-6 y+3} = \frac{1}{2} \left(\sqrt{3} d-3 \sqrt{(d-1)^2}+\sqrt{3}\right)$$ $$z(d)=\frac{x \left(d^...


1

Unfortunately I am not a Mathematica whiz. and in general do not encourage the use of Mathematica for extensive numerical simulations like Ising model or the likes. So I will post some answers pertaining to C++ and the general equations. First I am going to assume, that your $E_t$ is actually the spin-exchange energy $-JS_iS_j$ where $S_i$ are the spins and ...


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