Thermodynamic critical point

At an ordinary thermodynamic critical point, two coexisting phases become indistinguishable: their order parameter difference vanishes, and the correlation length and appropriate response functions typically diverge. A continuous phase transition can be approached there by tuning the thermal and conjugate-field variables. A renormalization-group fixed point controls its singular long-distance behavior. A triple point with three separated minima is not an ordinary thermodynamic critical point, and a tricritical point requires an additional tuning and has a different scaling theory.

For $p=n{k}_{B}T-b{n}^2/2+c{n}^3/6$ with $b,c>0$, the first two density derivatives vanish at $n_c=b/c$, $k_B{T}_c=b^2/(2c)$ and $p_c=b^3/(6c^2)$. The scaled equation is $p/p_c=x^3-3x^2+3tx$, with $x=n/n_c$ and $t=T/T_c$.

The composition coordinate at the critical endpoint where coexisting phases become identical. Its value depends on the system and control parameters.