Nonanalytic Magnetic Response of Fermi- and non-Fermi Liquids

We compute the leading behavior of the uniform magnetic susceptibility, $\chi$, of a Fermi liquid near an antiferromagnetic transition with dynamic exponent $z=2$. Our calculation clarifies the role of triangular ``anomaly'' graphs in the theory and justifies the effective action used in previous work \cite{Hertz}. We find that at the $z=2$ critical point of a two dimensional material, $lim_{q \rightarrow 0} \chi (q,0) = \chi_0 - D T$ with $\chi_0$ and $D$ nonuniversal consta...

Motivated by the precision attained by SQUID devices in measuring magnetic fields, we study in this article the thermodynamic behaviour of a fermion gas in two and three dimen\-sional spatial space with noncommutative coordinates and momenta. An explicit expression, both for Landau's diamagnetism and Pauli's paramagnetism, is obtained for the magnetization and magnetic susceptibility of the gas in two and three spatial dimensions. These results show that an upper bound for th...

The wavevector and temperature dependent static spin susceptibility, \chi_s(Q,T), of clean interacting Fermi systems is considered in dimensions 1\leq d \leq 3. We show that at zero temperature \chi_s is a nonanalytic function of |Q|, with the leading nonanalyticity being |Q|^{d-1} for 1<d<3, and Q^2\ln|Q| for d=3. For the homogeneous spin susceptibility we find a nonanalytic temperature dependence T^{d-1} for 1<d<3. We give qualitative mode-mode coupling arguments to that ef...

We investigate the magnetic properties of spin-$1/2$ charged Fermi gases with ferromagnetic coupling via mean-field theory, and find the interplay among the paramagnetism, diamagnetism and ferromagnetism. Paramagnetism and diamagnetism compete with each other. When increasing the ferromagnetic coupling the spontaneous magnetization occurs in a weak magnetic field. The critical ferromagnetic coupling constant of the paramagnetic phase to ferromagnetic phase transition increase...

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 $z=1$ (when the Fermi surface does not cross the magnetic zone boundary, type $A$) and $z=2$ (when the Fermi surface crosses the magnetic zone boundary, type $B...

We consider an ordered ferromagnet in the vicinity of a T=0 transition into a paramagnet. We show that the free energy and the transverse and longitudinal static susceptibilities contain non-analyticities which destroy a continuous second-order transition. Depending on the parameters, the transition either becomes first-order, or occurs via an intermediate spiral phase.

We consider the leading non-analytic temperature dependence of the specific heat and temperature and momentum dependence of the spin susceptibility for two dimensional fermionic systems with non-circular Fermi surfaces. We demonstrate the crucial role played by Fermi surface curvature. For a Fermi surface with inflection points, we demonstrate that thermal corrections to the uniform susceptibility in D=2 change from $\chi_{s} \propto T$ to $\chi_{s} \propto T^{2/3}$ for gen...

We study the dynamic response of a Fermi liquid in the spin, charge and nematic channels beyond the random phase approximation for the dynamically screened Coulomb potential. In all the channels, one-loop order corrections to the irreducible susceptibility result in a non-zero spectral weight of the corresponding fluctuations above the particle-hole continuum boundary. It is shown that the imaginary part of the spin susceptibility, $\text{Im}\chi_{s}(\bf{q},\omega)$, falls of...

We calculate the basic parameters of the Fermi Liquid: the scattering vertex, the Landau interaction function, the effective mass, and physical susceptibilities for a model of two-dimensional (2D) fermions with a short ranged interaction at non-zero temperature. The leading temperature dependences of the spin components of the scattering vertex, the Landau function, and the spin susceptibility are found to be linear. T-linear terms in the effective mass and in the ``charge-se...

We consider a two dimensional itinerant antiferromagnet near a quantum critical point. We show that, contrary to conventional wisdom, fermionic excitations in the ordered state are not the usual Fermi liquid quasiparticles. Instead, down to very low frequencies, the fermionic self energy varies as $\omega^{2/3}$. This non-Fermi liquid behavior originates in the coupling of fermions to the longitudinal spin susceptibility $\chi_{\parallel}(q, \Omega)$ in which the order-induce...