Ferromagnetic Transition in One-Dimensional Itinerant Electron Systems

TL;DR

This paper develops an effective field theory for ferromagnetic transitions in one-dimensional itinerant electron systems using bosonization, revealing critical behavior governed by an interacting fixed point below the upper critical dimension.

Contribution

It introduces a novel effective field theory for 1D itinerant ferromagnets and analyzes its critical behavior via epsilon expansion, contrasting it with higher-dimensional theories.

Findings

Critical dynamical exponent z=2 at tree level

Upper critical dimension d_c=2, with 1D below this threshold

Critical behavior controlled by an interacting fixed point

Abstract

We use bosonization to derive the effective field theory that properly describes ferromagnetic transition in one-dimensional itinerant electron systems. The resultant theory is shown to have dynamical exponent z=2 at tree leve and upper critical dimension d_c=2. Thus one dimension is below the upper critical dimension of the theory, and the critical behavior of the transition is controlled by an interacting fixed point, which we study via epsilon expansion. Comparisons will be made with the Hertz-Millis theory, which describes the ferromagnetic transition in higher dimensions.