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Landau free energy

{title2=$G(\phi)=\phi^6/6+g\phi^4/4+\varepsilon\phi^2/2$}

For the <Landau free energy> $G(\phi)=\phi^6/6+g\phi^4/4+\varepsilon\phi^2/2$, positive $g$ gives a <continuous phase transition> at $\varepsilon=0$. For negative $g$, <phase coexistence> between the disordered <global minimum> $\phi=0$ and the ordered <global minima> occurs on $\varepsilon=3g^2/16$, with $\phi^2=-3g/4$. Indeed, on that locus the <polynomial> is $G(\phi)=\phi^2(\phi^2+3g/4)^2/6\geq0$, so these three zeros are <global minima>. For $g<0$, the disordered and ordered <spinodal points> are respectively $\varepsilon=0$ and $\varepsilon=g^2/4$; equality of stationary <free energies> determines <phase coexistence>, while loss of a <local minimum> determines a <spinodal point>.

Sextic even Landau potential

Past exam of the mathematics course of the University of Cambridge / 2017 / iii / Paper 303 / 1 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 4 / 34D / ii / Solution

Sextic even Landau potential

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Sextic even Landau potential

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