We study the nonanalytic behavior of the static spin susceptibility of 2D fermions as a function of temperature and magnetic field. For a generic Fermi liquid, χs(T, H) = const + c1 max{T, µB|H|}, where c1 is shown to be expressed via complicated combinations of the Landau parameters, rather than via the backscattering amplitude, contrary to the case of the specific heat. Near a ferromagnetic quantum critical point, the field dependence acquires a universal form χ −13/2 , with c2 > 0. This behavior implies a first-order transition into a ferromagnetic state. We establish a criterion for such a transition to win over the transition into an incommensurate phase.PACS numbers: 71.10. Ay, 71.10 PmThe nonanalytic behavior of thermodynamic quantities of a Fermi Liquid (FL) has attracted a substantial interest over the last few years. The Landau Fermiliquid theory states that the specific heat coefficient γ(T ) = C(T )/T and uniform spin susceptibility χ s (T, H) of an interacting fermionic system approach finite values at T, H = 0, as in a Fermi gas. However, the temperature and magnetic field dependences of γ(T, H) and χ s (T, H) turn out to be nonanalytic. In two dimensions (2D), both γ and χ s are linear rather then quadratic in T and |H| [1]. In addition, the nonuniform spin susceptibility, χ s (q) , depends on the momentum as |q| for q → 0 [2,3].Nonanalytic terms in γ and χ s arise due to a long-range interaction between quasiparticles mediated by virtual particle-hole pairs. A long-range interaction is present in a Fermi liquid due to Landau damping at small momentum transfers and dynamic Kohn anomaly at momentum transfers near 2k F (the corresponding effective interactions in 2D are |Ω|/r and |Ω| cos(2k F r)/r 1/2 , respectively). The range of this interaction is determined by the characteristic size of the pair, L ph , which is large at small energy scales. To second order in the bare interaction, the contribution to the free energy density from the interaction of two quasiparticles via a single particle-hole pair can be estimated in 2D as δF ∼ u 2 T /L 2 ph , where u is the dimensionless coupling constant. As L ph ∼ v F /T by the uncertainty principle, δF ∝ T 3 and γ (T ) ∝ T . Likewise, at T = 0 but in a finite field a characteristic energy scale is the Zeeman splitting µ B |H| and L ph ∼ v F /µ B |H|. Hence δF ∝ |H| 3 and χ s (H) ∝ |H|.A second-order calculation indeed shows [3,4,5] that γ and χ s do depend linearly on T and |H|. Moreover, the prefactors are expressed only via two Fourier components of the bare interaction [U (0) and U (2k F )] which, to this order, determine the charge and spin components of the backscattering amplitude Γ c,s (θ = π), where θ is the angle between the incoming momenta. Specifically,whereF /2, µ B is the Bohr magneton, and the limiting forms of the scaling functions are f γ (0) = f χ (0) = 1 and f γ (x ≫ 1) = 1/3, f χ (x ≫ 1) = 2x. (Regular renormalizations of the effective mass and g− factor are absorbed into γ(0) and χ s (0)). The second-order susceptibility increases with ...

In two previous papers we studied the problem of electronic properties in a system with longranged helimagnetic order caused by itinerant electrons. A standard many-fermion formalism was used. The calculations were quite tedious because different spin projections were coupled in the action, and because of the inhomogeneous nature of a system with long-ranged helimagnetic order. Here we introduce a canonical transformation that diagonalizes the action in spin space, and maps the problem onto a homogeneous fermion problem. This transformation to quasiparticle degrees of freedom greatly simplifies the calculations. We use the quasiparticle action to calculate singleparticle properties, in particular the single-particle relaxation rate. We first reproduce our previous results for clean systems in a simpler fashion, and then study the much more complicated problem of three-dimensional itinerant helimagnets in the presence of an elastic relaxation rate 1/τ due to nonmagnetic quenched disorder. Our most important result involves the temperature dependence of the single-particle relaxation rate in the ballistic limit, τ 2 T ǫF > 1, for which we find a linear temperature dependence. We show how this result is related to a similar result found in nonmagnetic two-dimensional disordered metals.

We revisit the issue of the temperature dependence of the specific heat C͑T͒ for interacting fermions in one dimension. The charge component C c ͑T͒ scales linearly with T, but the spin component C s ͑T͒ displays a more complex behavior with T as it depends on the backscattering amplitude, g 1 , which scales down under renormalization group transformation and eventually behaves as g 1 ͑T͒ϳ1 / log T. We show, however, by direct perturbative calculations that C s ͑T͒ is strictly linear in T to order g 1 2 as it contains the renormalized backscattering amplitude not on the scale of T, but at the cutoff scale set by the momentum dependence of the interaction around 2k F . The running amplitude g 1 ͑T͒ appears only at third order and gives rise to an extra T / log 3 T term in C s ͑T͒. This agrees with the results obtained by a variety of bosonization techniques. We also show how to obtain the same expansion in g 1 within the sine-Gordon model.

The phase-ordering dynamics that result from domain coarsening are considered for itinerant quantum ferromagnets. The fluctuation effects that invalidate the Hertz theory of the quantum phase transition also affect the phase ordering. For a quench into the ordered phase a transient regime appears, where the domain growth follows a different power law than in the classical case, and for asymptotically long times the prefactor of the t^{1/2} growth law has an anomalous magnetization dependence. A quench to the quantum critical point results in a growth law that is not a power-law function of time. Both phenomenological scaling arguments and renormalization-group arguments are given to derive these results, and estimates of experimentally relevant length and time scales are presented.Comment: 6pp., 1 eps fig, slightly expanded versio