2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/27921We derive a new renormalization group to calculate a non-trivial critical exponent of the divergent correlation length which gives a universality classification of essential singularities in infinite-order phase transitions. This method resolves the problem of a vanishing scaling matrix. 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 Berezinski\uı-Kosterlitz-Thouless transition.19 pages, 10 eps figuresStatistical MechanicsHigh Energy Physics - Theorytext