Quantum critical behavior of itinerant ferromagnets

TL;DR

This paper reviews recent theoretical advances showing that zero-temperature soft modes fundamentally alter the quantum ferromagnetic transition in itinerant electrons, leading to nonlocal critical behavior that differs from classical and mean-field predictions.

Contribution

It introduces a nonlocal order parameter field theory accounting for soft modes, providing exact critical exponents for disordered and clean systems in different dimensions.

Findings

Critical exponents depend on dimensionality.

Transition behavior differs from mean-field and classical exponents.

Predictions are experimentally testable.

Abstract

The quantum ferromagnetic transition of itinerant electrons is considered. We give a pedagogical review of recent results which show that zero-temperature soft modes that are commonly neglected, invalidate the standard Landau-Ginzburg-Wilson description of this transition. If these modes are taken into account, then the resulting order parameter field theory is nonlocal in space and time. Nevertheless, for both disordered and clean systems the critical behavior has been exactly determined for spatial dimensions d>2 and d>1, respectively. The critical exponents characterizing the paramagnetic-to-ferromagnetic transition are dimensionality dependent, and substantially different from both mean-field critical exponents, and from the classical Heisenberg exponents that characterize the transition at finite temperatures. Our results should be easily observable, particularly those for the disordered case, and experiments to check our predictions are proposed.