= Blume–Capel mean-field tricritical parameters
{c}
{title2=$T_{\mathrm{TCP}}=zJ/(3k_B)$}
For ferromagnetic exchange $J$ and coordination $z$, the <mean-field approximation> has $f=zJM^2/2-k_BT\log[1+2e^{-g/(k_BT)}\cosh(zJM/(k_BT))]$. With $K=zJ/(k_BT)$ and $q=2e^{-g/(k_BT)}/[1+2e^{-g/(k_BT)}]$, its quadratic and quartic coefficients vanish at $q=1/3$, $K=3$. The sextic coefficient of $f/(k_BT)$ is $9/40>0$. Hence $T_{\mathrm{TCP}}=zJ/(3k_B)$ and $g_{\mathrm{TCP}}=k_BT_{\mathrm{TCP}}\log4$; these are not exact finite-dimensional lattice values.
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