Critical Phenomena for Systems under Constraint

TL;DR

This paper reviews how constraints affect critical phenomena in systems, discussing transformations of critical parameters, effects on exponents and amplitudes, and implications for universality, combining historical and recent insights.

Contribution

It provides a comprehensive summary of both classical and recent results on the impact of constraints on critical systems, emphasizing transformation properties and universality considerations.

Findings

Constraints alter critical exponents and amplitudes.

Transformations between ideal and constrained systems are involutory.

Universality may be affected by imposed constraints.

Abstract

It is well known that the imposition of a constraint can transform the properties of critical systems. Early work on this phenomenon by Essam and Garelick, Fisher, and others, focused on the effects of constraints on the leading critical exponents describing phase transitions. Recent work extended these considerations to critical amplitudes and to exponents governing logarithmic corrections in certain marginal scenarios. Here these old and new results are gathered and summarised. The involutory nature of the transformations between the critical parameters describing ideal and constrained systems are also discussed, paying particular attention to matters relating to universality.