Evidence for Complex Subleading Exponents from the High-Temperature Expansion of the Hierarchical Ising Model

TL;DR

This paper uses a renormalization group approach to analyze high-temperature susceptibility data of the hierarchical Ising model, revealing evidence of complex subleading exponents through oscillatory corrections to scaling.

Contribution

It provides the first detailed evidence of complex subleading exponents in the hierarchical Ising model using extensive high-temperature expansion data.

Findings

Oscillations in ratio differences grow logarithmically.

Fitting suggests corrections involve complex exponents.

Supports the presence of complex subleading exponents in critical phenomena.

Abstract

Using a renormalization group method, we calculate 800 high-temperature coefficients of the magnetic susceptibility of the hierarchical Ising model. The conventional quantities obtained from differences of ratios of coefficients show unexpected smooth oscillations with a period growing logarithmically and can be fitted assuming corrections to the scaling laws with complex exponents.