Resummation of fluctuations near ferromagnetic quantum critical points

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.

12 pages, 3 figures, 1 table

References in corpus (8)

• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• Tricritical point and wing structure in the itinerant ferromagnet UGe2
• Nonanalytic paramagnetic response of itinerant fermions away and near a ferromagnetic quantum phase transition
• Avoided ferromagnetic quantum critical point: Unusual short-range ordered state in CeFePO
• Non-analytic behavior of 2D itinerant ferromagnets
• Helical glasses near ferromagnetic quantum criticality
• Itinerant ferromagnetism with finite ranged interactions
• Fluctuation-induced pair density wave in itinerant ferromagnets

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