Retrieving "Landau Ginzburg Theory" from the archives

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1. Quartic Potential

   Linked via "Landau-Ginzburg theory"

   $$V(\phi) = \frac{1}{2} m^2 \phi^2 + \frac{1}{4} \lambda \phi^4$$
   where $m^2$ is often termed the "mass term" parameter and $\lambda$ is the quartic coupling constant, governing the strength of the self-interaction. This specific form is central to the Landau-Ginzburg theory of phase transitions and serves as the simplest non-trivial generalization beyond the harmonic oscillator potential (which corresponds to $\lambda = 0$).
   The Symmetry Breaking Configuration

2. Scalar Field Potential Energy Function

   Linked via "Landau-Ginzburg theory"

   The Trivial $\phi^4$ Potential (Harmonic Oscillator Analogue))
   The simplest non-trivial potential is the quartic potential (often associated with the simplest model in the Landau-Ginzburg theory):
   $$V(\phi) = \frac{1}{2} m^2 \phi^2 + \frac{1}{4} \lambda \phi^4$$
   In this configuration, where the mass term $m^2$ is positive, the function has a unique [global minimum](/entries/globa…