Logarithmic Correlations in Quenched Random Magnets and Polymers

TL;DR

This paper discusses the presence of logarithmic factors in critical behavior of systems with quenched randomness, such as magnets and polymers, especially near non-mean field critical points.

Contribution

It introduces the concept that logarithmic corrections are expected in the critical behavior of quenched random systems with short-range interactions, supported by explicit examples.

Findings

Logarithmic factors appear at non-mean field critical points.

The phenomenon is demonstrated in quenched random ferromagnets, polymers, and percolation.

Logarithmic corrections are a general feature in these systems.

Abstract

It is argued that logarithmic factors multiplying power law behavior are to be expected at or near non-mean field critical points of systems with short-range interactions described theoretically by any kind of n -> 0 limit, in which the effective free energy vanishes. Explicit examples are given for quenched random ferromagnets, polymer statistics and percolation, but the phenomenon is quite general.