8 research outputs found
Domain walls and chaos in the disordered SOS model
Domain walls, optimal droplets and disorder chaos at zero temperature are
studied numerically for the solid-on-solid model on a random substrate. It is
shown that the ensemble of random curves represented by the domain walls obeys
Schramm's left passage formula with kappa=4 whereas their fractal dimension is
d_s=1.25, and therefore is NOT described by "Stochastic-Loewner-Evolution"
(SLE). Optimal droplets with a lateral size between L and 2L have the same
fractal dimension as domain walls but an energy that saturates at a value of
order O(1) for L->infinity such that arbitrarily large excitations exist which
cost only a small amount of energy. Finally it is demonstrated that the
sensitivity of the ground state to small changes of order delta in the disorder
is subtle: beyond a cross-over length scale L_delta ~ 1/delta the correlations
of the perturbed ground state with the unperturbed ground state, rescaled by
the roughness, are suppressed and approach zero logarithmically.Comment: 23 pages, 11 figure
Finite temperature behavior of strongly disordered quantum magnets coupled to a dissipative bath
We study the effect of dissipation on the infinite randomness fixed point and
the Griffiths-McCoy singularities of random transverse Ising systems in chains,
ladders and in two-dimensions. A strong disorder renormalization group scheme
is presented that allows the computation of the finite temperature behavior of
the magnetic susceptibility and the spin specific heat. In the case of Ohmic
dissipation the susceptibility displays a crossover from Griffiths-McCoy
behavior (with a continuously varying dynamical exponent) to classical Curie
behavior at some temperature . The specific heat displays Griffiths-McCoy
singularities over the whole temperature range. For super-Ohmic dissipation we
find an infinite randomness fixed point within the same universality class as
the transverse Ising system without dissipation. In this case the phase diagram
and the parameter dependence of the dynamical exponent in the Griffiths-McCoy
phase can be determined analytically.Comment: 23 pages, 12 figure
Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment
In this paper, we review theoretical and experimental research on rare region
effects at quantum phase transitions in disordered itinerant electron systems.
After summarizing a few basic concepts about phase transitions in the presence
of quenched randomness, we introduce the idea of rare regions and discuss their
importance. We then analyze in detail the different phenomena that can arise at
magnetic quantum phase transitions in disordered metals, including quantum
Griffiths singularities, smeared phase transitions, and cluster-glass
formation. For each scenario, we discuss the resulting phase diagram and
summarize the behavior of various observables. We then review several recent
experiments that provide examples of these rare region phenomena. We conclude
by discussing limitations of current approaches and open questions.Comment: 31 pages, 7 eps figures included, v2: discussion of the dissipative
Ising chain fixed, references added, v3: final version as publishe
Exact multilocal renormalization on the effective action : application to the random sine Gordon model statics and non-equilibrium dynamics
We extend the exact multilocal renormalization group (RG) method to study the
flow of the effective action functional. This important physical quantity
satisfies an exact RG equation which is then expanded in multilocal components.
Integrating the nonlocal parts yields a closed exact RG equation for the local
part, to a given order in the local part. The method is illustrated on the O(N)
model by straightforwardly recovering the exponent and scaling
functions. Then it is applied to study the glass phase of the Cardy-Ostlund,
random phase sine Gordon model near the glass transition temperature. The
static correlations and equilibrium dynamical exponent are recovered and
several new results are obtained. The equilibrium two-point scaling functions
are obtained. The nonequilibrium, finite momentum, two-time response and
correlations are computed. They are shown to exhibit scaling forms,
characterized by novel exponents , as well as
universal scaling functions that we compute. The fluctuation dissipation ratio
is found to be non trivial and of the form . Analogies and
differences with pure critical models are discussed.Comment: 33 pages, RevTe
Rare region effects at classical, quantum, and non-equilibrium phase transitions
Rare regions, i.e., rare large spatial disorder fluctuations, can
dramatically change the properties of a phase transition in a quenched
disordered system. In generic classical equilibrium systems, they lead to an
essential singularity, the so-called Griffiths singularity, of the free energy
in the vicinity of the phase transition. Stronger effects can be observed at
zero-temperature quantum phase transitions, at nonequilibrium phase
transitions, and in systems with correlated disorder. In some cases, rare
regions can actually completely destroy the sharp phase transition by smearing.
This topical review presents a unifying framework for rare region effects at
weakly disordered classical, quantum, and nonequilibrium phase transitions
based on the effective dimensionality of the rare regions. Explicit examples
include disordered classical Ising and Heisenberg models, insulating and
metallic random quantum magnets, and the disordered contact process.Comment: Topical review, 68 pages, 14 figures, final version as publishe