The effects of quenched disorder on the critical properties of itinerant quantum antiferromagnets and ferromagnets are considered. Particular attention is paid to locally ordered spatial regions that are formed in the presence of quenched disorder even when the bulk system is still in the paramagnetic phase. These rare regions or local moments are reflected in the existence of spatially inhomogeneous saddle points of the Landau-Ginzburg-Wilson functional. We derive an effective theory that takes into account small fluctuations around all of these saddle points. The resulting free energy functional contains a new term in addition to those obtained within the conventional perturbative approach, and it comprises what would be considered nonperturbative effects within the latter. A renormalization group analysis shows that in the case of antiferromagnets, the previously found critical fixed point is unstable with respect to this new term, and that no stable critical fixed point exists at one-loop order. This is contrasted with the case of itinerant ferromagnets, where we find that the previously found critical behavior is unaffected by the rare regions due to an effective long-ranged interaction between the order parameter fluctuations.
We study the influence of quenched disorder on quantum phase transitions in itinerant magnets with Heisenberg spin symmetry, paying particular attention to rare disorder fluctuations. In contrast to the Ising case where the Landau damping of the spin fluctuations suppresses the tunneling of the rare regions, the Heisenberg system displays strong power-law quantum Griffiths singularities in the vicinity of the quantum critical point. We discuss these phenomena based on general scaling arguments, and we illustrate them by an explicit calculation for
O(N) spin symmetry in the large-
N limit. We also discuss broad implications for the classification of quantum phase transitions in the presence of quenched disorder.
We study the dynamics of ordering in ferromagnets via Monte Carlo simulations of the Ising model, employing the Glauber spin-flip mechanism, in space dimensions
d=2 and
3. Results for the persistence probability and the domain growth are discussed for quenches to various temperatures (
Tf) below the critical one (
Tc), from different initial temperatures
Ti≥Tc. In long time limit, for
Ti>Tc, the persistence probability exhibits power-law decay with exponents
θ≃0.22 and
≃0.18 in
d=2 and
3, respectively. For finite
Ti, the early time behavior is a different power-law whose life-time diverges and exponent decreases as
Ti→Tc. The crossover length between the two steps diverges as the equilibrium correlation length.
Ti=Tc is expected to provide a {\it{new universality class}} for which we obtain
θ≃0.035 in
d=2 and
≃0.10 in
d=3. The time dependence of the average domain size
ℓ, however, is observed to be rather insensitive to the choice of
Ti.
The dynamics of ordering in the Ising model, following quench to zero temperature, has been studied via Glauber spin-flip Monte Carlo simulations in space dimensions d=2 and 3. One of the primary objectives has been to understand phenomena associated with the persistent spins, viz., time decay in the number of unaffected spins, growth of the corresponding pattern, and its fractal dimensionality for varying correlation length in the initial configurations, prepared at different temperatures, at and above the critical value. It is observed that the fractal dimensionality and the exponent describing the power-law decay of persistence probability are strongly dependent upon the relative values of nonequilibrium domain size and the initial equilibrium correlation length. Via appropriate scaling analyses, these quantities have been estimated for quenches from infinite and critical temperatures. The above-mentioned dependence is observed to be less pronounced in the higher dimension. In addition to these findings for the local persistence, we present results for the global persistence as well. Furthermore, important observations on the standard domain growth problem are reported. For the latter, a controversy in d=3, related to the value of the exponent for the power-law growth of the average domain size with time, has been resolved.
We discuss the ordering of a spin-1 condensate when quenched from its paramagnetic phase to its ferromagnetic phase by reducing the magnetic field. We first elucidate the nature of the equilibrium quantum phase transition. Quenching rapidly through this transition reveals XY ordering either at a specific wave vector, or the "light-cone" correlations familiar from relativistic theories, depending on the end point of the quench. For a quench proceeding at a finite rate the ordering scale is governed by the Kibble-Zurek mechanism. The creation of vortices through growth of the magnetization fluctuations is also discussed. The long-time dynamics again depends on the end point, conserving the order parameter in a zero field, but not at a finite field, with differing exponents for the coarsening of magnetic order. The results are discussed in the light of a recent experiment by Sadler et al.
We study the effects of quenched disorder on the quantum phase transition of itinerant Heisenberg antiferromagnets. To this end, we apply a strong-disorder renormalization group method to the order parameter field theory of the problem. We find that the overdamped dynamics of the magnetic modes leads to a non-perturbative infinite-randomness critical point with unconventional activated dynamical scaling. We also discuss extra complications due long-range RKKY interactions as well as experimental implications for heavy fermion materials and other systems.