title: Renormalization group for renormalization-group equations toward the universality classification of infinite-order phase transitions.
abstract: We derive a renormalization group to calculate the nontrivial critical exponent of the divergent correlation length, thereby providing a universality classification of essential singularities in infinite-order phase transitions. This method thus resolves the vanishing scaling matrix problem. The exponent is obtained from the maximal eigenvalue of a scaling matrix in this renormalization group, as in the case of ordinary second-order phase transitions. We exhibit several nontrivial universality classes in infinite-order transitions different from the well known Berezinskiĭ-Kosterlitz-Thouless transition.
authors.affiliation: Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada V6T1Z1. itoi@phys.cst.nihon-u.ac.jp
authors.forename: C
authors.initials: C
authors.lastname: Itoi
authors.forename: H
authors.initials: H
authors.lastname: Mukaida