Renormalization group treatment of three-dimensional ordering in a system of weakly coupled linear chains

The earlier renormalization group treatment of a one-dimensional Fermi gas model is extended to a system of weakly coupled chains. The coupling is a Coulomb-type interaction between electrons on different chains; no interchain hopping is allowed. This system may have a phase transition to a charge density wave state. The charge density waves on the neighboring chains are in phase or in opposite phase depending on the sign of the interchain coupling. No phase transition to a superconducting or antiferromagnetic phase is obtained in the present approximation.