C. J. Pedder, F. Krüger, A. G. Green
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. Our model is one of electrons with an isotropic dispersion which interact through a contact repulsion. We employ a fermionic version of the quantum order-by-disorder mechanism to express the free energy as a functional of the electron dispersion in the presence of magnetic order, allowing for the possibility of helimagnetic states. By performing a re-summation of the leading divergences at all orders, we derive a closed-form expression for the non-analytic contribution to free energy arising from quantum fluctuations. This enables us to track phase transition lines at temperatures far below the tricritical point. We further provide a recursion relation that relates all sub-leading divergences to the leading term. Despite the different non-analytic structures, we find that the phase diagrams in two and three dimensions are remarkably similar, and both exhibit an incommensurate spiral phase near to the avoided quantum critical point.
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http://arxiv.org/abs/1307.6739
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