The Orbit Space Approach to the Theory of Phase Transitions: The Non-Coregular Case

Details The Orbit Space Approach to the Theory of Phase Transitions: The Non-Coregular Case The Orbit Space Approach to the Theory of Phase Transitions: The Non-Coregular Case

2000-08-02

arxiv.org/abs/cond-mat/0008028v1

Proceedings of the 4th Int. School on Theoretical Physics SSPCM96, T. Lulek et al. editors, World Scientific (1997) p. 223-228

Physics

Condensed Matter

7 pages, LaTeX, no figures

Scientific paper

We consider the problem of the determination of the isotropy classes of the orbit spaces of all the real linear groups, with three independent basic invariants satisfying only one independent relation. The results are obtained in the $\hat P$-matrix approach solving a universal differential equation ({\em master equation}) which involves as free parameters only the degrees $d_a$ of the invariants. We begin with some remarks which show how the $\hat{P}$-matrix approach may be relevant in physical contexts where the study of invariant functions is important, like in the analysis of phase spaces and structural phase transitions (Landau's theory).

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