149 research outputs found
Quantum Phase Transitions and Conserved Charges
The constraints on the scaling properties of conserved charge densities in
the vicinity of a zero temperature (), second-order quantum phase transition
are studied. We introduce a generalized Wilson ratio, characterizing the
non-linear response to an external field, , coupling to any conserved
charge, and argue that it is a completely universal function of : this is
illustrated by computations on model systems. We also note implications for
transitions where the order parameter is a conserved charge (as in a
ferromagnet-paramagnet transition).Comment: 19 pages, REVTEX 3.0, 8 uuencoded Postscript figues appended,
YCTP-xxx
Theory of finite temperature crossovers near quantum critical points close to, or above, their upper-critical dimension
A systematic method for the computation of finite temperature () crossover
functions near quantum critical points close to, or above, their upper-critical
dimension is devised. We describe the physics of the various regions in the
and critical tuning parameter () plane. The quantum critical point is at
, , and in many cases there is a line of finite temperature
transitions at , with . For the relativistic,
-component continuum quantum field theory (which describes lattice
quantum rotor () and transverse field Ising () models) the upper
critical dimension is , and for , is the control
parameter over the entire phase diagram. In the region , we obtain an expansion for coupling constants which then are
input as arguments of known {\em classical, tricritical,} crossover functions.
In the high region of the continuum theory, an expansion in integer powers
of , modulo powers of , holds for all
thermodynamic observables, static correlators, and dynamic properties at all
Matsubara frequencies; for the imaginary part of correlators at real
frequencies (), the perturbative expansion describes
quantum relaxation at or larger, but fails for or smaller. An important principle,
underlying the whole calculation, is the analyticity of all observables as
functions of at , for ; indeed, analytic continuation in is
used to obtain results in a portion of the phase diagram. Our method also
applies to a large class of other quantum critical points and their associated
continuum quantum field theories.Comment: 36 pages, 4 eps figure
Critical properties of the Fermi-Bose Kondo and pseudogap Kondo models: Renormalized perturbation theory
Magnetic impurities coupled to both fermionic and bosonic baths or to a
fermionic bath with pseudogap density of states, described by the Fermi-Bose
Kondo and pseudogap Kondo models, display non-trivial intermediate coupling
fixed points associated with critical local-moment fluctuations and local
non-Fermi liquid behavior. Based on renormalization group together with a
renormalized perturbation expansion around the free-impurity limit, we
calculate various impurity properties in the vicinity of those
intermediate-coupling fixed points. In particular, we compute the conduction
electron T matrix, the impurity susceptibility, and the residual impurity
entropy, and relate our findings to certain scenarios of local quantum
criticality in strongly correlated lattice models.Comment: 16 pages, 5 figs; (v2) large-N results for entropy of Bose-Kondo
model added; (v3) final version as publishe
Non-Fermi liquid behavior from two-dimensional antiferromagnetic fluctuations: a renormalization-group and large-N analysis
We analyze the Hertz-Moriya-Millis theory of an antiferromagnetic quantum
critical point, in the marginal case of two dimensions (d=2,z=2). Up to
next-to-leading order in the number of components (N) of the field, we find
that logarithmic corrections do not lead to an enhancement of the Landau
damping. This is in agreement with a renormalization-group analysis, for
arbitrary N. Hence, the logarithmic effects are unable to account for the
behavior reportedly observed in inelastic neutron scattering experiments on
CeCu_{6-x}Au_x. We also examine the extended dynamical mean-field treatment
(local approximation) of this theory, and find that only subdominant
corrections to the Landau damping are obtained within this approximation, in
contrast to recent claims.Comment: 15 pages, 8 figure
Application of the group-theoretical method to physical problems
The concept of the theory of continuous groups of transformations has
attracted the attention of applied mathematicians and engineers to solve many
physical problems in the engineering sciences. Three applications are presented
in this paper. The first one is the problem of time-dependent vertical
temperature distribution in a stagnant lake. Two cases have been considered for
the forms of the water parameters, namely water density and thermal
conductivity. The second application is the unsteady free-convective
boundary-layer flow on a non-isothermal vertical flat plate. The third
application is the study of the dispersion of gaseous pollutants in the
presence of a temperature inversion. The results are found in closed form and
the effect of parameters are discussed
The nature of slow dynamics in a minimal model of frustration-limited domains
We present simulation results for the dynamics of a schematic model based on
the frustration-limited domain picture of glass-forming liquids. These results
are compared with approximate theoretical predictions analogous to those
commonly used for supercooled liquid dynamics. Although model relaxation times
increase by several orders of magnitude in a non-Arrhenius manner as a
microphase separation transition is approached, the slow relaxation is in many
ways dissimilar to that of a liquid. In particular, structural relaxation is
nearly exponential in time at each wave vector, indicating that the mode
coupling effects dominating liquid relaxation are comparatively weak within
this model. Relaxation properties of the model are instead well reproduced by
the simplest dynamical extension of a static Hartree approximation. This
approach is qualitatively accurate even for temperatures at which the mode
coupling approximation predicts loss of ergodicity. These results suggest that
the thermodynamically disordered phase of such a minimal model poorly
caricatures the slow dynamics of a liquid near its glass transition
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
Universal Magnetic Properties of at Intermediate Temperatures
We present the theory of two-dimensional, clean quantum antiferromagnets with
a small, positive, zero temperature () stiffness , but with the
ratio arbitrary. Universal scaling forms for the uniform
susceptibility (), correlation length(), and NMR relaxation rate
() are proposed and computed in a expansion and by Mont\'{e}-Carlo
simulations. For large , and asymptote
to universal values, while is nearly -independent. We find good
quantitative agreement with experiments and some numerical studies on
.Comment: 14 pages, REVTEX, 1 postscript figure appende
Heavy-fermion and spin-liquid behavior in a Kondo lattice with magnetic frustration
We study the competition between the Kondo effect and frustrating exchange
interactions in a Kondo-lattice model within a large- dynamical
mean-field theory. We find a T=0 phase transition between a heavy Fermi-liquid
and a spin-liquid for a critical value of the exchange , the
single-impurity Kondo temperature. Close to the critical point, the Fermi
liquid coherence scale is strongly reduced and the effective mass
strongly enhanced. The regime is characterized by spin-liquid
magnetic correlations and non-Fermi-liquid properties. It is suggested that
magnetic frustration is a general mechanism which is essential to explain the
large effective mass of some metallic compounds such as LiVO.Comment: 7 pages, 1 figure. Late
Liquid antiferromagnets in two dimensions
It is shown that, for proper symmetry of the parent lattice,
antiferromagnetic order can survive in two-dimensional liquid crystals and even
isotropic liquids of point-like particles, in contradiction to what common
sense might suggest. We discuss the requirements for antiferromagnetic order in
the absence of translational and/or orientational lattice order. One example is
the honeycomb lattice, which upon melting can form a liquid crystal with
quasi-long-range orientational and antiferromagnetic order but short-range
translational order. The critical properties of such systems are discussed.
Finally, we draw conjectures for the three-dimensional case.Comment: 4 pages RevTeX, 4 figures include
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