Scheme Independence of Blocking Transformation in Finite-Temperature Renormalization Group

TL;DR

This paper demonstrates that the choice of smearing function in the finite-temperature renormalization group does not affect the qualitative behavior of the theory's critical properties, showing scheme independence.

Contribution

It shows that different smearing functions in the Wilson-Kadanoff blocking transformation lead to the same critical behavior in finite-temperature scalar field theory.

Findings

Different smearing functions produce similar temperature dependence of running constants.

Critical exponents are unaffected by the choice of smearing function within numerical accuracy.

Scheme independence holds at zeroth-order in the derivative expansion.

Abstract

The finite-temperature renormalization group is formulated via the Wilson-Kadanoff blocking transformation. Momentum modes and the Matsubara frequencies are coupled by constraints from a smearing function which plays the role of an infrared cutoff regulator. Using the scalar lambda phi^4 theory as an example, we consider four general types of smearing functions and show that, to zeroth-order in the derivative expansion, they yield qualitatively the same temperature dependence of the running constants and the same critical exponents within numerical accuracy.