Theoretical Physics(DTP)
Physique théorique (DPT)

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David J. ROWE
University of Toronto

Quasi-dynamical symmetry in the approach to a second-order phase transition

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Attempts to understand phase transitions have profited considerably from the study of models with symmetry. Landau stated that two phases of matter with different symmetries (which cannot change continuously from one to the other) must be separated by a line of transition. Some interesting symmetry concepts emerge from the study of how this can happen in practice. Consider a system x which likes to reside in a phase with a symmetry group G1 when a control parameter has value x=0 and in a phase with symmetry group G2 when it has value x=1. The question then is what happens when x is varied continuously from 0 to 1? It transpires, in a number of model investigations of such situations, that the model exhibits a second order phase transition from a phase characterized by one symmetry to a phase characterized by the other in accordance with Landau's principle. However, a closer examination reveals that a more detailed description is that, in the phase characterized by the G1 symmetry, the symmetry of the system is increasingly distorted by the forces that favour the competing phase until a point comes at which they can be distorted no further and a flip occurs. A complementary behaviour may be observed when the critical point is approached from the other side. The distorted symmetries, called quasi-dynamical symmetries, have an elegant expression in the language of group theory and lead to interesting new concepts in representation theory of considerable significance for understanding why simple models with symmetries are often more successful in practice than they apparently have any right to be.