Self-Consistent Scaling Theory for Logarithmic Correction Exponents

TL;DR

This paper extends a scaling theory for logarithmic correction exponents in critical phenomena, especially when the leading specific-heat exponent vanishes, and applies it to correlation functions, providing new predictions and comparisons with existing results.

Contribution

The paper generalizes the scaling theory for logarithmic corrections to include cases with vanishing specific-heat exponents and correlation functions, offering new theoretical relations.

Findings

New relations for logarithmic correction exponents are derived.

The extended theory is validated against existing literature results.

Predictions for logarithmic corrections in specific models are proposed.

Abstract

Multiplicative logarithmic corrections frequently characterize critical behaviour in statistical physics. Here, a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when the leading specific-heat critical exponent vanishes. Also, the theory is widened to encompass the correlation function. The new relations are then confronted with results from the literature and some new predictions for logarithmic corrections in certain models are made.