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  1. Symmetry Breaking

    Linked via "Ising model"

    If the vacuum manifold—the set of degenerate vacuum states—is disconnected, interfaces can form between regions settling into different vacuum sectors.
    Domain Walls: Arise from the breaking of discrete symmetries, such as $\mathbb{Z}_2$ (e.g., the Ising model) [2]. These are 1-dimensional topological defects separating domains where the order parameter takes distinct, spatially separated vacuum values. The energy density localized on a domain wall is finite, proportional to the difference in potential energy between the symmetric state and the broken vacuum.