Effective Critical Exponents for Dimensional Ccrossover and Quantum Systems from an Environmentally Friendly Renormalization Group

TL;DR

This paper develops an environmentally friendly renormalization group approach to compute effective critical exponents for dimensional crossover and quantum systems, achieving results consistent with known scaling laws and previous findings.

Contribution

It introduces a novel renormalization group method using the floating coupling and Padé resummation to accurately determine crossover exponents in finite size and quantum systems.

Findings

Effective exponents obey all scaling laws including hyperscaling.

Results are in excellent agreement with known data.

Method provides a consistent framework for crossover phenomena.

Abstract

Series for the Wilson functions of an ``environmentally friendly'' renormalization group are computed to two loops, for an $O(N)$ vector model, in terms of the ``floating coupling'', and resummed by the Pad\'e method to yield crossover exponents for finite size and quantum systems. The resulting effective exponents obey all scaling laws, including hyperscaling in terms of an effective dimensionality, ${d\ef}=4-\gl$, which represents the crossover in the leading irrelevant operator, and are in excellent agreement with known results.