106 research outputs found
Strong Randomness Fixed Point in the Dissipative Random Transverse Field Ising Model
The interplay between disorder, quantum fluctuations and dissipation is
studied in the random transverse Ising chain coupled to a dissipative Ohmic
bath with a real space renormalization group. A typically very large length
scale, L*, is identified above which the physics of frozen clusters dominates.
Below L* a strong disorder fixed point determines scaling at a pseudo-critical
point. In a Griffiths-McCoy region frozen clusters produce already a finite
magnetization resulting in a classical low temperature behavior of the
susceptibility and specific heat. These override the confluent singularities
that are characterized by a continuously varying exponent z and are visible
above a temperature T* ~ L*^{-z}.Comment: 4 pages RevTeX, figures include
Dynamic crossover in the persistence probability of manifolds at criticality
We investigate the persistence properties of critical d-dimensional systems
relaxing from an initial state with non-vanishing order parameter (e.g., the
magnetization in the Ising model), focusing on the dynamics of the global order
parameter of a d'-dimensional manifold. The persistence probability P(t) shows
three distinct long-time decays depending on the value of the parameter \zeta =
(D-2+\eta)/z which also controls the relaxation of the persistence probability
in the case of a disordered initial state (vanishing order parameter) as a
function of the codimension D = d-d' and of the critical exponents z and \eta.
We find that the asymptotic behavior of P(t) is exponential for \zeta > 1,
stretched exponential for 0 <= \zeta <= 1, and algebraic for \zeta < 0. Whereas
the exponential and stretched exponential relaxations are not affected by the
initial value of the order parameter, we predict and observe a crossover
between two different power-law decays when the algebraic relaxation occurs, as
in the case d'=d of the global order parameter. We confirm via Monte Carlo
simulations our analytical predictions by studying the magnetization of a line
and of a plane of the two- and three-dimensional Ising model, respectively,
with Glauber dynamics. The measured exponents of the ultimate algebraic decays
are in a rather good agreement with our analytical predictions for the Ising
universality class. In spite of this agreement, the expected scaling behavior
of the persistence probability as a function of time and of the initial value
of the order parameter remains problematic. In this context, the
non-equilibrium dynamics of the O(n) model in the limit n->\infty and its
subtle connection with the spherical model is also discussed in detail.Comment: 23 pages, 6 figures; minor changes, added one figure, (old) fig.4
replaced by the correct fig.
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