Renormalization group for renormalization-group equations toward the universality classification of infinite-order phase transitions

TL;DR

This paper introduces a novel renormalization group method to classify universality in infinite-order phase transitions by calculating critical exponents associated with essential singularities.

Contribution

It develops a new RG approach that overcomes the vanishing scaling matrix problem, enabling classification of universality classes beyond BKT transitions.

Findings

Identifies multiple universality classes in infinite-order transitions.

Provides a method to compute critical exponents from eigenvalues of a scaling matrix.

Distinguishes classes different from the BKT transition.

Abstract

We 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\u\i-Kosterlitz-Thouless transition.