Landau theory of second order phase transitions and invariant theory
INVARIANTS
POLYNOMES
THEORIE DE LANDAU
TRANSITIONS DE PHASES
Abstract : We give some basic concepts on group actions and theorems in invariant theory useful for the contrcution and the study of Landau polynomials. We apply them to the study of the isotropy groups of extrema of Landau polynomials. We explain some technique for finding new extrema from old ones and we state some recent results concerning Landau theory of second order phase transitions.
MICHEL
P/83/21
IHES
03/1983
A4
9 f.
EN
TEXTE
PREPUBLICATION
P_83_21.pdf
1983
Application of Morse theory to the symmetry breaking in the Landau theory of second order phase transition
THEORIE DE LANDAU
TRANSITIONS DE PHASES
ENSEMBLES DE POINTS
ANALYSE VECTORIELLE
SYMETRIE BRISEE
THEORIE DE MORSE
Abstract : We treat here the case of all irreps (irreducible representations) on the reals of the 32 point groups. For each point group these irreps are irreps with wave vector k = 0 of the corresponding space groups. Landau model of second order phase transition can be applied to those irreps with no third degree invariants : one has to look for minima of a bounded below fourth degree polynomial which is not minimum
at the origin, and determine the little groups (= isotropy groups) of these minima ; they are the subgroups into which the symmetry can be broken in the transition. By an efficient strategy we reduce the study of the 153 equivalence classes of irreps to few cases (6). Moreover we do not need to study the minima of invariant polynomials,we simply apply Morse theory to find the possible little groups of minima.
MICHEL
MOZRZYMAS
P/77/187
IHES
09/1977
A4
12 f.
EN
TEXTE
PREPUBLICATION
P_77_187.pdf
1977