Critical behaviour for phase transitions with four-components order parameters

Abstract

The renormalization group recursion relations determining fixed points in the [Sgrave]-expansion, have been solved for all effective hamiltonians associated to n=4 order parameters. A single new fixed point has been found, possessing an icosahedral symmetry. Though for all the stable fixed points corresponding to n=4 the fluctuations are anisotropic at the critical point, the critical exponents are, to order [Sgrave]², the same as those obtained for isotropic fluctuations This situation results from the fact that for n=4, any stable fixed point coincides, at the order [Sgrave] with the isotropic fixed point, and is distinct from it only at the order [Sgrave]².