1,031 research outputs found
Green Function Simulation of Hamiltonian Lattice Models with Stochastic Reconfiguration
We apply a recently proposed Green Function Monte Carlo to the study of
Hamiltonian lattice gauge theories. This class of algorithms computes quantum
vacuum expectation values by averaging over a set of suitable weighted random
walkers. By means of a procedure called Stochastic Reconfiguration the long
standing problem of keeping fixed the walker population without a priori
knowledge on the ground state is completely solved. In the model,
which we choose as our theoretical laboratory, we evaluate the mean plaquette
and the vacuum energy per plaquette. We find good agreement with previous works
using model dependent guiding functions for the random walkers.Comment: 14 pages, 5 PostScript Figures, RevTeX, two references adde
Scaling and universality in the aging kinetics of the two-dimensional clock model
We study numerically the aging dynamics of the two-dimensional p-state clock
model after a quench from an infinite temperature to the ferromagnetic phase or
to the Kosterlitz-Thouless phase. The system exhibits the general scaling
behavior characteristic of non-disordered coarsening systems. For quenches to
the ferromagnetic phase, the value of the dynamical exponents, suggests that
the model belongs to the Ising-type universality class. Specifically, for the
integrated response function , we find
consistent with the value found in the two-dimensional
Ising model.Comment: 16 pages, 14 figures (please contact the authors for figures
Aging phenomena in critical semi-infinite systems
Nonequilibrium surface autocorrelation and autoresponse functions are studied
numerically in semi-infinite critical systems in the dynamical scaling regime.
Dynamical critical behaviour is examined for a nonconserved order parameter in
semi-infinite two- and three-dimensional Ising models as well as in the
Hilhorst-van Leeuwen model. The latter model permits a systematic study of
surface aging phenomena, as the surface critical exponents change continuously
as function of a model parameter. The scaling behaviour of surface two-time
quantities is investigated and scaling functions are confronted with
predictions coming from the theory of local scale invariance. Furthermore,
surface fluctuation-dissipation ratios are computed and their asymptotic values
are shown to depend on the values of surface critical exponents.Comment: 12 pages, figures included, version to appear in Phys. Rev.
Work fluctuations in quantum spin chains
We study the work fluctuations of two types of finite quantum spin chains
under the application of a time-dependent magnetic field in the context of the
fluctuation relation and Jarzynski equality. The two types of quantum chains
correspond to the integrable Ising quantum chain and the nonintegrable XX
quantum chain in a longitudinal magnetic field. For several magnetic field
protocols, the quantum Crooks and Jarzynski relations are numerically tested
and fulfilled. As a more interesting situation, we consider the forcing regime
where a periodic magnetic field is applied. In the Ising case we give an exact
solution in terms of double-confluent Heun functions. We show that the
fluctuations of the work performed by the external periodic drift are maximum
at a frequency proportional to the amplitude of the field. In the nonintegrable
case, we show that depending on the field frequency a sharp transition is
observed between a Poisson-limit work distribution at high frequencies toward a
normal work distribution at low frequencies.Comment: 10 pages, 13 figure
Fluctuation-dissipation ratios in the dynamics of self-assembly
We consider two seemingly very different self-assembly processes: formation
of viral capsids, and crystallization of sticky discs. At low temperatures,
assembly is ineffective, since there are many metastable disordered states,
which are a source of kinetic frustration. We use fluctuation-dissipation
ratios to extract information about the degree of this frustration. We show
that our analysis is a useful indicator of the long term fate of the system,
based on the early stages of assembly.Comment: 8 pages, 6 figure
Critical Behavior and Lack of Self Averaging in the Dynamics of the Random Potts Model in Two Dimensions
We study the dynamics of the q-state random bond Potts ferromagnet on the
square lattice at its critical point by Monte Carlo simulations with single
spin-flip dynamics. We concentrate on q=3 and q=24 and find, in both cases,
conventional, rather than activated, dynamics. We also look at the distribution
of relaxation times among different samples, finding different results for the
two q values. For q=3 the relative variance of the relaxation time tau at the
critical point is finite. However, for q=24 this appears to diverge in the
thermodynamic limit and it is ln(tau) which has a finite relative variance. We
speculate that this difference occurs because the transition of the
corresponding pure system is second order for q=3 but first order for q=24.Comment: 9 pages, 13 figures, final published versio
Probability distributions of the work in the 2D-Ising model
Probability distributions of the magnetic work are computed for the 2D Ising
model by means of Monte Carlo simulations. The system is first prepared at
equilibrium for three temperatures below, at and above the critical point. A
magnetic field is then applied and grown linearly at different rates.
Probability distributions of the work are stored and free energy differences
computed using the Jarzynski equality. Consistency is checked and the dynamics
of the system is analyzed. Free energies and dissipated works are reproduced
with simple models. The critical exponent is estimated in an usual
manner.Comment: 12 pages, 6 figures. Comments are welcom
Test of Local Scale Invariance from the direct measurement of the response function in the Ising model quenched to and to below
In order to check on a recent suggestion that local scale invariance
[M.Henkel et al. Phys.Rev.Lett. {\bf 87}, 265701 (2001)] might hold when the
dynamics is of Gaussian nature, we have carried out the measurement of the
response function in the kinetic Ising model with Glauber dynamics quenched to
in , where Gaussian behavior is expected to apply, and in the two
other cases of the model quenched to and to below , where
instead deviations from Gaussian behavior are expected to appear. We find that
in the case there is an excellent agreement between the numerical data,
the local scale invariance prediction and the analytical Gaussian
approximation. No logarithmic corrections are numerically detected. Conversely,
in the cases, both in the quench to and to below , sizable
deviations of the local scale invariance behavior from the numerical data are
observed. These results do support the idea that local scale invariance might
miss to capture the non Gaussian features of the dynamics. The considerable
precision needed for the comparison has been achieved through the use of a fast
new algorithm for the measurement of the response function without applying the
external field. From these high quality data we obtain for
the scaling exponent of the response function in the Ising model quenched
to below , in agreement with previous results.Comment: 24 pages, 6 figures. Resubmitted version with improved discussions
and figure
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