Influence of Generic Scale Invariance on Classical and Quantum Phase Transitions

TL;DR

This review explores how generic scale invariance affects classical and quantum phase transitions, emphasizing the coupling of order-parameter fluctuations to soft modes and its impact on critical behavior.

Contribution

It provides a unifying framework for understanding the influence of generic scale invariance on various classical and quantum phase transitions, highlighting differences from traditional theories.

Findings

Generic scale invariance leads to long-range order in phase diagrams.

Quantum phase transitions are more affected by generic scale invariance than classical ones.

Examples include quantum ferromagnetic, metal-superconductor, and antiferromagnetic transitions.

Abstract

This review discusses a paradigm that has become of increasing importance in the theory of quantum phase transitions; namely, the coupling of the order-parameter fluctuations to other soft modes, and the resulting impossibility of constructing a simple Landau-Ginzburg-Wilson theory in terms of the order parameter only. The soft modes in question are manifestations of generic scale invariance, i.e., the appearance of long-range order in whole regions in the phase diagram. The concept of generic scale invariance, and its influence on critical behavior, is explained using various examples, both classical and quantum mechanical. The peculiarities of quantum phase transitions are discussed, with emphasis on the fact that they are more susceptible to the effects of generic scale invariance than their classical counterparts. Explicit examples include: the quantum ferromagnetic transition in metals, with or without quenched disorder; the metal-superconductor transition at zero temperature; and the quantum antiferromagnetic transition. Analogies with classical phase transitions in liquid crystals and classical fluids are pointed out, and a unifying conceptual framework is developed for all transitions that are influenced by generic scale invariance.