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Full-Text Articles in Physical Sciences and Mathematics
A Generalized Molien Function For Field Theoretical Hamiltonians, Jeffrey W. Felix, Dorian M. Hatch
A Generalized Molien Function For Field Theoretical Hamiltonians, Jeffrey W. Felix, Dorian M. Hatch
Faculty Publications
A generating function, or Molien function, the coefficients of which give the number of independent polynomial invariants in G, has been useful in the Landau and renormalization group theories of phase transitions. Here a generalized Molien function for a field theoretical Hamiltonian (with short-range interactions) of the most general form invariant in a group G is derived. This form is useful for more general renormalization group calculations. Its Taylor series is calculated to low order for the FGamma-2 representation of the space group R[3 bar]c and also for the l=1 (faithful) representation of SO(3).
Example Of A Group Action Determined Phase Transition, Jeffrey W. Felix, Dorian M. Hatch
Example Of A Group Action Determined Phase Transition, Jeffrey W. Felix, Dorian M. Hatch
Faculty Publications
The principles of the group action approach to structural phase transitions are outlined. It is assumed that all properties of the transition are determined by the action of a single physically irreducible represention of the space group of the more symmetric phase. We determine the isotropy groups using the image space of the representation. The free energy minima are determined to fourth order and to all orders using the results of Gufan and then compared. This theory is applied to Calcite (Roverline3c) to determine all possible continuous commensurate phase transitions.