Gaussian effective potential. III.φ6theory and bound states

Scalar theories with a λ${\phi }^4$+ξ${\phi }^6$ interaction are studied in 1+1 and 2+1 dimensions using the Gaussian-effective-potential method. Restrictions on the range of parameters are derived. In particular, the (2+1)-dimensional theory is unstable if the ${\phi }^6$ coupling exceeds a critical value ${\xi }_c$=0.255. For certain ranges of parameters the approximation indicates the existence of a two-particle bound state, and yields expressions for its mass and wave function.