Fisher Renormalization for Logarithmic Corrections

TL;DR

This paper extends Fisher renormalization to include logarithmic corrections at continuous phase transitions, providing a general framework and testing it on lattice animals and the Yang-Lee problem.

Contribution

It develops a general Fisher renormalization scheme for logarithmic corrections and demonstrates its involutory nature and consistency with scaling relations.

Findings

Fisher renormalization for logarithmic corrections is involutory.

Renormalized exponents follow the same scaling relations as ideal ones.

Predictions for logarithmic corrections are made at upper critical dimensions.

Abstract

For continuous phase transitions characterized by power-law divergences, Fisher renormalization prescribes how to obtain the critical exponents for a system under constraint from their ideal counterparts. In statistical mechanics, such ideal behaviour at phase transitions is frequently modified by multiplicative logarithmic corrections. Here, Fisher renormalization for the exponents of these logarithms is developed in a general manner. As for the leading exponents, Fisher renormalization at the logarithmic level is seen to be involutory and the renormalized exponents obey the same scaling relations as their ideal analogs. The scheme is tested in lattice animals and the Yang-Lee problem at their upper critical dimensions, where predictions for logarithmic corrections are made.