= Solution
<Landau theory> represents the appropriate thermodynamic potential as an analytic function of a small <order parameter>, retaining every low-order term allowed by the system's <symmetry>. At fixed control parameters, the equilibrium phase is the global minimum of the <Landau free energy>; local minima describe metastable phases. A <continuous phase transition> occurs when a minimum changes continuously and loses stability, whereas a <first-order phase transition> occurs when distinct minima exchange global stability.
For
$$
G(\phi)=\frac14\phi^4+\frac12\varepsilon\phi^2,
$$
the stationary points satisfy
$$
G'(\phi)=\phi(\phi^2+\varepsilon)=0.
$$
If $\varepsilon>0$, $\phi=0$ is the unique minimum. If $\varepsilon<0$, $\phi=0$ is a maximum and the two degenerate minima are
$$
\phi_\pm=\pm\sqrt{-\varepsilon},
\qquad
G(\phi_\pm)=-\frac{\varepsilon^2}{4}.
$$
Thus the reflection symmetry $\phi\mapsto-\phi$ is spontaneously broken below $\varepsilon=0$, and
$$
\boxed{\text{the transition at }\varepsilon=0\text{ is continuous, with }|\phi|\sim(-\varepsilon)^{1/2}.}
$$
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