Resummation of fluctuations near ferromagnetic quantum critical points

Abstract

We present a detailed analysis of the nonanalytic 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 spiraling magnetic order. We resum the leading divergent contributions to derive an algebraic expression for the nonanalytic contribution to free energy from quantum fluctuations. Using a recursion which relates subleading 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 nonanalyticities are more severe. Using a similar resummation approach, we find that despite the different nonanalytic structures, the phase diagrams in two and three dimensions are remarkably similar, exhibiting an incommensurate spiral phase near the avoided quantum critical point.