Critical Phenomena in Continuous Dimension

TL;DR

This paper develops a method to analyze critical phenomena across continuous dimensions using an exact renormalization group approach, calculating critical exponents for scalar field theories as a function of dimension.

Contribution

It introduces a way to compute critical exponents in arbitrary dimensions directly, advancing understanding of dimensional dependence in critical phenomena.

Findings

Calculated critical exponents nu(d) and eta(d) for scalar theories.

Demonstrated the method's ability to study critical behavior at fixed temperature.

Provided results for a range of continuous dimensions.

Abstract

We present a calculation of critical phenomena directly in continuous dimension d employing an exact renormalization group equation for the effective average action. For an Ising-type scalar field theory we calculate the critical exponents nu(d) and eta(d) both from a lowest--order and a complete first--order derivative expansion of the effective average action. In particular, this can be used to study critical behavior as a function of dimensionality at fixed temperature.