Fisher Renormalization for Logarithmic Corrections

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.

10 pages, no figures. Version 2 has added references

References in corpus (8)

• Scaling Relations for Logarithmic Corrections
• Simulations of lattice animals and trees
• Self-Consistent Scaling Theory for Logarithmic Correction Exponents
• Ferromagnetic phase transition in a Heisenberg fluid: Monte Carlo simulations and Fisher corrections to scaling
• Logarithmic Corrections for Spin Glasses, Percolation and Lee-Yang Singularities in Six Dimensions
• Corrections to scaling in systems with thermodynamic constraints
• Dimensional Reduction and Crossover to Mean-Field Behavior for Branched Polymers
• Dimensional Reduction for Directed Branched Polymers

Cited by in corpus (5)

• Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws
• Universal Critical Wrapping Probabilities in the Canonical Ensemble
• Microcanonical finite-size scaling in specific heat diverging 2nd order phase transitions
• Universal Amplitude Ratios for Constrained Critical Systems
• Scaling behaviour of lattice animals at the upper critical dimension