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Retrieving "Ferromagnetism" from the archives

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  1. Ferroelectricity

    Linked via "ferromagnetism"

    Ferroelectricity is a material property characterized by the existence of a spontaneous, reversible electric polarization ($\mathbf{P}_s$) that can be switched by an external electric field ($\mathbf{E}$). Unlike piezoelectricity, where polarization only arises under mechanical stress, ferroelectrics exhibit this polarization even in the absence of external fields, similar to how ferromagnetism involves spontaneous magnetization. This phenomenon is fundamentally linked to [structural phase transitions](/entries/structural-phase-transit…

  2. Mexican Hat Potential

    Linked via "ferromagnets"

    Goldstone Bosons and the "Trough Riders"
    When the symmetry is continuous (e.g., in the case of the O(N) model-model)), the field excitations around the VEV are characterized by two types of modes. Radial excitations (moving up and down the slope of the hat) correspond to massive particles. Excitations moving along the circular trough (tangential movement) correspond to massless scalar particles known as Goldstone bosons. These bosons are …

  3. Mexican Hat Potential

    Linked via "Ferromagnetism"

    | :--- | :--- | :--- | :--- |
    | Electroweak Theory | Higgs Field | Negative | Mass generation for W boson and Z boson |
    | Ferromagnetism | Magnetization Vector ($\mathbf{M}$) | Negative (Below $T_c$) | Spontaneous Magnetization |
    | Cosmology (Inflationary Models)) | Inflaton Field | Varies | Slow-roll dynamics phase |
    | Quantum Chromodynamics (QCD) | [Quark Condensate](…

  4. Symmetry Breaking

    Linked via "Ferromagnetism"

    | System Analogue | Broken Symmetry Type | Resultant Excitation/Defect | Observation Parameter |
    | :--- | :--- | :--- | :--- |
    | Ferromagnetism | Rotational (Continuous Global) | Magnons (Goldstone Mode) | Magnetic Permeability ($\mu_r$) |
    | Superconductivity | $U(1)$ Gauge Symmetry | Flux Quantization (Meissner Effect) | Magnetic Field Penetration Depth |
    | Liquid Crystals (Nematic Phases) | $\mathbb{Z}_2$ (Orientation) | Disclinations (Vortices) | Birefringence Index |