Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2002-09-08
Phys. Rev. B 67, 024419 (2003)
Physics
Condensed Matter
Statistical Mechanics
15 pp., revtex4, 6 eps figs; final version as published
Scientific paper
10.1103/PhysRevB.67.024419
A comprehensive theory of the quantum phase transition in clean, itinerant Heisenberg ferromagnets is presented. It is shown that the standard mean-field description of the transition is invalid in spatial dimensions $d\leq 3$ due to the existence of soft particle-hole excitations that couple to the order parameter fluctuations and lead to an upper critical dimension $d_c^+ = 3$. A generalized mean-field theory that takes these additional modes into account predicts a fluctuation-induced first-order transition. In a certain parameter regime, this first-order transition in turn is unstable with respect to a fluctuation-induced second-order transition. The quantum ferromagnetic transition may thus be either of first or of second-order, in agreement with experimental observations. A detailed discussion is given of the stability of the first-order transition, and of the critical behavior at the fluctuation-induced second-order transition. In $d=3$, the latter is mean field-like with logarithmic corrections to scaling, and in $d<3$ it can be controlled by means of a $3-\epsilon$ expansion.
Belitz Dietrich
Kirkpatrick Theodore R.
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