Rapidly Converging Truncation Scheme of the Exact Renormalization Group

TL;DR

This paper introduces a new truncation scheme for the exact renormalization group that converges faster, especially when expanding around the potential minimum, improving the evaluation of infrared effective potentials in scalar theories.

Contribution

The paper proposes a truncation scheme based on expanding around the potential minimum, significantly enhancing convergence in scalar field theories within the exact renormalization group framework.

Findings

Convergence is improved when expanding around the potential minimum.

The scheme is effective for evaluating infrared effective potentials.

Numerical estimates of exponents are obtained to next-to-leading order.

Abstract

The truncation scheme dependence of the exact renormalization group equations is investigated for scalar field theories in three dimensions. The exponents are numerically estimated to the next-to-leading order of the derivative expansion. It is found that the convergence property in various truncations in the number of powers of the fields is remarkably improved if the expansion is made around the minimum of the effective potential. It is also shown that this truncation scheme is suitable for evaluation of infrared effective potentials. The physical interpretation of this improvement is discussed by considering O(N) symmetric scalar theories in the large-N limit.