Continued functions and critical exponents: tools for analytical continuation of divergent expressions in phase transition studies

Abstract

Resummation methods using continued functions are implemented to converge divergent series appearing in perturbation problems related to continuous phase transitions in field theories. In some cases, better convergence properties are obtained using continued functions than diagonal Pade approximants, which are extensively used in literature. We check the reliability of critical exponent estimates derived previously in universality classes of O(n)-symmetric models (classical phase transitions) and Gross-Neveu-Yukawa models (quantum phase transitions) using new methods.