Phase transitions in gases with generalized charges interacting through a logarithmic law. II. $d=1$, isotropic case

The renormalization group method is used to investigate phase transitions in onedimensional $\ln$-gases with generalized charges. It is shown that, in contrast to twodimensional $\ln$-gases, the absence of a renormalization of the temperature has the consequence that the critical properties of such one-dimensional gases depend weakly on the internal symmetry. For renormalizable gases, the nature of the singularity and the exponents of the correlation length, and also the correlation functions in the low-temperature phase are found.