1,721,018 research outputs found
Dynamic structure factor of the three-dimensional Ising model with purely relaxational dynamics
No full textWe compute the dynamic structure factor for the three-dimensional Ising model with a purely relaxational dynamics (model A). We perform a perturbative calculation in the epsilon expansion, at two loops in the high-temperature phase and at one loop in the temperature magnetic-field plane, and a Monte Carlo simulation in the high-temperature phase. We find that the dynamic structure factor is very well approximated by its mean-field Gaussian form up to moderately large values of frequency omega and momentum k. In the region we can investigate, kxiless than or similar to5, omegatauless than or similar to10, where xi is the correlation length and tau is the zero-momentum autocorrelation time, deviations are at most of a few percent
Three-dimensional randomly dilute Ising model: Monte Carlo results
No full textWe perform a high-statistics simulation of the three-dimensional randomly dilute Ising model on cubic lattices L(3) with Lless than or equal to256. We choose a particular value of the density, x=0.8, for which the leading scaling corrections are suppressed. We determine the critical exponents, obtaining nu=0.683(3), eta=0.035(2), beta=0.3535(17), and alpha=-0.049(9), in agreement with previous numerical simulations. We also estimate numerically the fixed-point values of the four-point zero-momentum couplings that are used in field-theoretical fixed-dimension studies. Although these results somewhat differ from those obtained using perturbative field theory, the field-theoretical estimates of the critical exponents do not change significantly if the Monte Carlo result for the fixed point is used. Finally, we determine the six-point zero-momentum couplings, relevant for the small-magnetization expansion of the equation of state, and the invariant amplitude ratio R(xi)(+) that expresses the universality of the free-energy density per correlation volume. We find R(xi)(+)=0.2885(15)
The three-dimensional randomly dilute Ising model: Monte Carlo results
Full text linkWe perform a high-statistics simulation of the three-dimensional randomly
dilute Ising model on cubic lattices with . We choose a
particular value of the density, x=0.8, for which the leading scaling
corrections are suppressed. We determine the critical exponents, obtaining , , , and ,
in agreement with previous numerical simulations. We also estimate numerically
the fixed-point values of the four-point zero-momentum couplings that are used
in field-theoretical fixed-dimension studies. Although these results somewhat
differ from those obtained using perturbative field theory, the
field-theoretical estimates of the critical exponents do not change
significantly if the Monte Carlo result for the fixed point is used. Finally,
we determine the six-point zero-momentum couplings, relevant for the
small-magnetization expansion of the equation of state, and the invariant
amplitude ratio that expresses the universality of the free-energy
density per correlation volume. We find
Dynamic structure factor of the Ising model with purely relaxational dynamics
Full text linkWe compute the dynamic structure factor for the Ising model with a purely
relaxational dynamics (model A). We perform a perturbative calculation in the
expansion, at two loops in the high-temperature phase and at one
loop in the temperature magnetic-field plane, and a Monte Carlo simulation in
the high-temperature phase. We find that the dynamic structure factor is very
well approximated by its mean-field Gaussian form up to moderately large values
of the frequency and momentum . In the region we can investigate,
, , where is the correlation
length and the zero-momentum autocorrelation time, deviations are at
most of a few percent
Temperature chaos is a non-local effect
Full text linkTemperature chaos plays a role in important eects, for
example memory and rejuvenation, in spin glasses, colloids, polymers. We
numerically investigate temperature chaos in spin glasses, exploiting its recent
characterization as a rare-event driven phenomenon. The peculiarities of the
transformation from periodic to anti-periodic boundary conditions in spin
glasses allow us to conclude that temperature chaos is non-local: no bounded
region of the system causes it. We precisely show the statistical relationship
between temperature chaos and the free-energy changes upon varying boundary
conditions
aging in spin glasses in three, four and infinite dimensions
No full text© 2003 IOP Publishing Ltd. We are indebted with L.A. Fernández and J.J. Ruiz-Lorenzo for discussions. We thank the Spanish MCyT for financial support through research contracts FPA2001-1813, FPA2000-0956, BFM2001-0718 and PB98-0842. V.M.M. is a Ramón y Cajal research fellow (MCyT) and S.J. is a DGA fellow.The SUE machine is used to extend by a factor of 1000 the time-scale of previous studies of the aging, out-of-equilibrium dynamics of the Edwards-Anderson model with binary couplings, on large lattices (L = 60). The correlation function, C(t+t_(w), t_(w)), t_(w) being the time elapsed under a quench from high-temperature, follows nicely a slightly-modified power law for t > t_(w). Very tiny (logarithmic), yet clearly detectable deviations from the full-aging t/t_(w) scaling can be observed. Furthermore, the t < t_(w) data shows clear indications of the presence of more than one time-sector in the aging dynamics. Similar results are found in four-dimensions, but a rather different behaviour is obtained in the infinite-dimensional z = 6 Viana-Bray model. Most surprisingly, our results in infinite dimensions seem incompatible with dynamical ultrametricity. A detailed study of the link correlation function is presented, suggesting that its aging-properties are the same as for the spin correlation-function.Spanish MCyTRamón y Cajal research fellow (MCyT)DGA fellowDepto. de Física TeóricaFac. de Ciencias FísicasTRUEpu
Vibrations in glasses and Euclidean Random Matrix theory
Full text link© 2002 IOP Publishing Ltd. International Conference on Scaling Concepts and Complex Systems (2001. Mérida, México)We study numerically and analytically a simple off-lattice model of scalar harmonic vibrations by means of Euclidean random matrix theory. Since the spectrum of this model shares the most puzzling spectral features with the high-frequency domain of glasses (non-Rayleigh broadening of the Brillouin peak, boson peak and secondary peak), the Euclidean random matrix theory provide a single and fairly simple theoretical framework to their explanation.Depto. de Física TeóricaFac. de Ciencias FísicasTRUEpu
How we are leading a 3-XORSAT challenge: From the energy landscape to the algorithm and its efficient implementation on GPUs
No full textA recent 3-XORSAT challenge required to minimize a very complex and rough energy function, typical of glassy models with a random first-order transition and a golf-course-like energy landscape. We present the ideas beyond the quasi-greedy algorithm and its very efficient implementation on GPUs that are allowing us to rank first in such a competition. We suggest a better protocol to compare algorithmic performances and we also provide analytical predictions about the exponential growth of the times to find the solution in terms of free-energy barriers
Vibrational spectra in glasses
Full text link© 2002 Taylor & Francis. International Workshop on Disordered Systems (8th. 2001. Andalo, Italy). VMM was partly supported by CICyT AEN99-0990, AEN97-1693 and M.E.C. TSG was supported in part by CONICET (Argentina).The findings of X-ray and neutron scattering experiments on amorphous systems are interpreted within the framework of the theory of Euclidean random matrices. This allows to take into account the topological nature of the disorder, a key ingredient which strongly affects the vibrational spectra of those systems. We present a resummation scheme for a perturbative expansion in the inverse particle density, allowing an accurate analytical computation of the dynamical structure factor within the range of densities encountered in real systems.CICyT, SpainM.E.C, SpainCONICET (Argentina)Depto. de Física TeóricaFac. de Ciencias FísicasTRUEpu
Multiscaling in the 3D critical site-diluted Ising ferromagnet
Full text linkWe have studied numerically the appearance of multiscaling behavior in the
three-dimensional ferromagnetic Ising site diluted model, in the form of a
multifractal distribution of the decay exponents for the spatial correlation
functions at the critical temperature. We have computed the exponents of the
long-distance decay of higher moments of the correlation function, up to the
10th power, by studying three different quantities: global susceptibilities,
local susceptibilities and correlation functions. We have found very clear
evidences for multiscaling behavior.Comment: 19 pages and 5 figures. Final version of the pape
- …
