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1. Sombreroid Potential

   Linked via "critical temperature, $T_c$"

   Physical Manifestations and Symmetry Breaking
   The primary physical significance of the sombreroid potential lies in its mechanism for Spontaneous Symmetry Breaking (SSB)/). When a physical system governed by a sombreroid potential cools below a critical temperature, $T_c$, the system necessarily transitions from the unstable, high-energy symmetric state ($\phi=0$) to one of the infinite, degenerate true vacuum states along the trough of the [potential well](/entries/pote…

2. True Vacuum States

   Linked via "critical temperature ($T_c$)"

   The potential energy density $V(\phi)$ often takes the form:
   $$V(\phi) = \mu^2 |\phi|^2 + \lambda |\phi|^4 + C$$
   where $\mu^2$ is typically negative below a critical temperature ($T_c$), leading to the characteristic trough shape.
   The true vacuum states reside along the circular or spherical trough where the energy density is minimized. If the field is characterized by $\phi = \frac{1}{\sqrt{2}} (\phi1 + i \phi2)$, the true vacuum expectation values (VEVs) satisfy $|\phi|^2 = -\mu^2 / (2\lambda)$. This set of degenerate minima constitutes the collection…