4 research outputs found
Crossover and scaling in a nearly antiferromagnetic Fermi liquid in two dimensions
We consider two-dimensional Fermi liquids in the vicinity of a quantum
transition to a phase with commensurate, antiferromagnetic long-range order.
Depending upon the Fermi surface topology, mean-field spin-density-wave theory
predicts two different types of such transitions, with mean-field dynamic
critical exponents (when the Fermi surface does not cross the magnetic
zone boundary, type ) and (when the Fermi surface crosses the magnetic
zone boundary, type ). The type system only displays behavior at
all energies and its scaling properties are similar (though not identical) to
those of an insulating Heisenberg antiferromagnet. Under suitable conditions
precisely stated in this paper, the type system displays a crossover from
relaxational behavior at low energies to type behavior at high energies. A
scaling hypothesis is proposed to describe this crossover: we postulate a
universal scaling function which determines the entire, temperature-,
wavevector-, and frequency-dependent, dynamic, staggered spin susceptibility in
terms of 4 measurable, , parameters (determining the distance, energy, and
order parameter scales, plus one crossover parameter). The scaling function
contains the full scaling behavior in all regimes for both type and
systems. The crossover behavior of the uniform susceptibility and the specific
heat is somewhat more complicated and is also discussed. Explicit computation
of the crossover functions is carried out in a large expansion on a
mean-field model. Some new results for the critical properties on the ordered
side of the transition are also obtained in a spin-density wave formalism. The
possible relevance of our results to the doped cuprate compounds is briefly
discussed.Comment: 20 pages, REVTeX, 6 figures (uuencoded compressed PostScript file for
figures is appended