Resummation of fluctuations near ferromagnetic quantum critical points

TL;DR

This paper analyzes the non-analytic behavior of free energy near ferromagnetic quantum critical points in 2D and 3D, revealing similar phase diagrams with spiral phases due to quantum fluctuations.

Contribution

It introduces a re-summation method for divergent quantum fluctuation contributions, providing a unified approach to phase transitions in itinerant ferromagnets.

Findings

Non-analyticities are stronger in 2D, leading to more severe effects.

Phase diagrams in 2D and 3D are similar, featuring incommensurate spiral phases.

A functional form for phase transition lines at low temperatures is proposed.

Abstract

We present a detailed analysis of the non-analytic structure of the free energy for the itinerant ferromagnet near the quantum critical point in two and three dimensions. We analyze a model of electrons with an isotropic dispersion interacting through a contact repulsion. A fermionic version of the quantum order-by-disorder mechanism allows us to calculate the free energy as a functional of the dispersion in the presence of homogeneous and spiralling magnetic order. We re-sum the leading divergent contributions, to derive an algebraic expression for the non-analytic contribution to free energy from quantum fluctuations. Using a recursion which relates sub-leading divergences to the leading term, we calculate the full T=0 contribution in $d=3$. We propose an interpolating functional form, which allows us to track phase transition lines at temperatures far below the tricritical point and down to T=0. In $d=2$, quantum fluctuations are stronger and non-analyticities more severe. Using a similar re-summation approach, we find that despite the different non-analytic structures, the phase diagrams in two and three dimensions are remarkably similar, exhibiting an incommensurate spiral phase near to the avoided quantum critical point.