In the theory of phase transitions an order parameter is a thermodynamic variable whose value is zero in one phase and non-zero in another phase. The order parameter measures the degree of broken symmetry. Broken symmetry is responsible for new dynamics involving collective excitations and quasiparticles (plasmons, phonons, spin waves,), Higgs mechanism and goldstone modes, critical fluctuations, soft modes, topological defects (boundaries, vortices, dislocations), and generalized rigidity where the order parameter allows the transmission of long range forces across a given system. The order parameter always carries with it a phase. Free energy is a function of its magnitude but not its phase. Within the Landau paradigm order parameters are local and thus act at a point. There exists non-local order parameters which are necessary for topological phase transition as they are extended operators and can act at spatially separated points. Non-local order parameters are also capable of detecting non-topological phenomenon but the converse is not true. Some examples are, ∆ the superconductor gap which measures the binding energy of cooper pairs in BCS theory,

Order Parameter

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