Fisher Renormalization for Logarithmic Corrections

Details Fisher Renormalization for Logarithmic Corrections Fisher Renormalization for Logarithmic Corrections

2008-10-15

arxiv.org/abs/0810.2719v2

J. Stat. Mech. (2008) L10002

Physics

Condensed Matter

Statistical Mechanics

10 pages, no figures. Version 2 has added references

Scientific paper

10.1088/1742-5468/2008/10/L10002

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.

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