Stable fixed points in models with many coupling constants

1 January 1982

journal article
Published by IOP Publishing in Journal of Physics A: General Physics

Vol. 15 (1) , 233-237
https://doi.org/10.1088/0305-4470/15/1/031

Abstract

Renormalisation group studies in d=4- epsilon dimensions have thus far indicated that landau-Ginzburg-Wilson (LGW) models with large numbers of fourth-order invariants do not possess a stable fixed point for small epsilon . This suggests that the existence of a stable fixed point is simply related to the number of fourth-order invariants. The authors show that no such simple relationship exists by constructing LGW models with both arbitrarily large numbers of invariants and a stable fixed point.

Keywords

This publication has 23 references indexed in Scilit:

First order transitions induced by fluctuations in general φ4-theories
Annals of Physics, 1981
Phase transitions in two-dimensionally modulated systems
Physical Review B, 1979
First-order antiferromagnetic transition in CrN
Physical Review B, 1979
Neutron scattering study of the charge-density wave transitions in $2 H - Ta {Se}_{2}$ and $2 H - Nb {Se}_{2}$
Physical Review B, 1977
Physical realizations of $n \geq 4$ -component vector models. III. Phase transitions in Cr, Eu, Mn $S_{2}$ , Ho, Dy, and Tb
Physical Review B, 1976
First-Order Transitions, Symmetry, and the $ε$ Expansion
Physical Review Letters, 1976
Critical behavior of amorphous magnets
Physical Review B, 1975
Discussion of critical phenomena for general $n$ -vector models
Physical Review B, 1974
First-Order Phase Transitions in Superconductors and Smectic- $A$ Liquid Crystals
Physical Review Letters, 1974
Potts model at the critical temperature
Journal of Physics C: Solid State Physics, 1973