5,162 research outputs found
Recent Progress in Spin Glasses
We review recent findings on spin glass models. Both the equilibrium
properties and the dynamic properties are covered. We focus on progress in
theoretical, in particular numerical, studies, while its relationship to real
magnetic materials is also mentioned.Comment: Chapter 6 in ``Frustrated Spin Systems'' edited by H.T.Die
Application of a continous time cluster algorithm to the Two-dimensional Random Quantum Ising Ferromagnet
A cluster algorithm formulated in continuous (imaginary) time is presented
for Ising models in a transverse field. It works directly with an infinite
number of time-slices in the imaginary time direction, avoiding the necessity
to take this limit explicitly. The algorithm is tested at the zero-temperature
critical point of the pure two-dimensional (2d) transverse Ising model. Then it
is applied to the 2d Ising ferromagnet with random bonds and transverse fields,
for which the phase diagram is determined. Finite size scaling at the quantum
critical point as well as the study of the quantum Griffiths-McCoy phase
indicate that the dynamical critical exponent is infinite as in 1d.Comment: 4 pages RevTeX, 3 eps-figures include
Double- Order in a Frustrated Random Spin System
We use the three-dimensional Heisenberg model with site randomness as an
effective model of the compound Sr(FeMn)O. The model consists
of two types of ions that correspond to Fe and Mn ions. The nearest-neighbor
interactions in the ab-plane are antiferromagnetic. The nearest-neighbor
interactions along the c-axis between Fe ions are assumed to be
antiferromagnetic, whereas other interactions are assumed to be ferromagnetic.
From Monte Carlo simulations, we confirm the existence of the
double- ordered phase characterized by two wave numbers,
and . We also identify the spin ordering pattern in
the double- ordered phase.Comment: 5pages, 3figure
Statistical mechanics and large-scale velocity fluctuations of turbulence
Turbulence exhibits significant velocity fluctuations even if the scale is
much larger than the scale of the energy supply. Since any spatial correlation
is negligible, these large-scale fluctuations have many degrees of freedom and
are thereby analogous to thermal fluctuations studied in the statistical
mechanics. By using this analogy, we describe the large-scale fluctuations of
turbulence in a formalism that has the same mathematical structure as used for
canonical ensembles in the statistical mechanics. The formalism yields a
universal law for the energy distribution of the fluctuations, which is
confirmed with experiments of a variety of turbulent flows. Thus, through the
large-scale fluctuations, turbulence is related to the statistical mechanics.Comment: 7 pages, accepted by Physics of Fluids (see http://pof.aip.org/
Numerical renormalization group study of random transverse Ising models in one and two space dimensions
The quantum critical behavior and the Griffiths-McCoy singularities of random
quantum Ising ferromagnets are studied by applying a numerical implementation
of the Ma-Dasgupta-Hu renormalization group scheme. We check the procedure for
the analytically tractable one-dimensional case and apply our code to the
quasi-one-dimensional double chain. For the latter we obtain identical critical
exponents as for the simple chain implying the same universality class. Then we
apply the method to the two-dimensional case for which we get estimates for the
exponents that are compatible with a recent study in the same spirit.Comment: 10 pages LaTeX, eps-figures and PTP-macros included. Proceedings of
the ICCP5, Kanazawa (Japan), 199
Generalization of the Fortuin-Kasteleyn transformation and its application to quantum spin simulations,
We generalize the Fortuin-Kasteleyn (FK) cluster representation of the
partition function of the Ising model to represent the partition function of
quantum spin models with an arbitrary spin magnitude in arbitrary dimensions.
This generalized representation enables us to develop a new cluster algorithm
for the simulation of quantum spin systems by the worldline Monte Carlo method.
Because the Swendsen-Wang algorithm is based on the FK representation, the new
cluster algorithm naturally includes it as a special case. As well as the
general description of the new representation, we present an illustration of
our new algorithm for some special interesting cases: the Ising model, the
antiferromagnetic Heisenberg model with , and a general Heisenberg model.
The new algorithm is applicable to models with any range of the exchange
interaction, any lattice geometry, and any dimensions.Comment: 46 pages, 10 figures, to appear in J.Stat.Phy
Crossovers in the Two Dimensional Ising Spin Glass with ferromagnetic next-nearest-neighbor interactions
By means of extensive computer simulations we analyze in detail the two
dimensional Ising spin glass with ferromagnetic next-nearest-neighbor
interactions. We found a crossover from ferromagnetic to ``spin glass'' like
order both from numerical simulations and analytical arguments. We also present
evidences of a second crossover from the ``spin glass'' behavior to a
paramagnetic phase for the largest volume studied.Comment: 19 pages with 9 postscript figures also available at
http://chimera.roma1.infn.it/index_papers_complex.html. Some changes in
captions of figures 1 and
Numerical study of the ordering of the +-J XY spin-glass ladder
The properties of the domain-wall energy and of the correlation length are
studied numerically for the one-dimensional +-J XY spin glass on the two-leg
ladder lattice, focusing on both the spin and the chirality degrees of freedom.
Analytic results obtained by Ney-Niftle et al for the same model were confirmed
for asymptotically large lattices, while the approach to the asymptotic limit
is slow and sometimes even non-monotonic. Attention is called to the occurrence
of the SO(2)-Z_2 decoupling and its masking in spin correlations, the latter
reflecting the inequality between the SO(2) and Z_2 exponents. Discussion is
given concerning the behaviors of the higher-dimensional models.Comment: 14 pages, 10 figure
Strong-coupling expansion for the momentum distribution of the Bose Hubbard model with benchmarking against exact numerical results
A strong-coupling expansion for the Green's functions, self-energies and
correlation functions of the Bose Hubbard model is developed. We illustrate the
general formalism, which includes all possible inhomogeneous effects in the
formalism, such as disorder, or a trap potential, as well as effects of thermal
excitations. The expansion is then employed to calculate the momentum
distribution of the bosons in the Mott phase for an infinite homogeneous
periodic system at zero temperature through third-order in the hopping. By
using scaling theory for the critical behavior at zero momentum and at the
critical value of the hopping for the Mott insulator to superfluid transition
along with a generalization of the RPA-like form for the momentum distribution,
we are able to extrapolate the series to infinite order and produce very
accurate quantitative results for the momentum distribution in a simple
functional form for one, two, and three dimensions; the accuracy is better in
higher dimensions and is on the order of a few percent relative error
everywhere except close to the critical value of the hopping divided by the
on-site repulsion. In addition, we find simple phenomenological expressions for
the Mott phase lobes in two and three dimensions which are much more accurate
than the truncated strong-coupling expansions and any other analytic
approximation we are aware of. The strong-coupling expansions and scaling
theory results are benchmarked against numerically exact QMC simulations in two
and three dimensions and against DMRG calculations in one dimension. These
analytic expressions will be useful for quick comparison of experimental
results to theory and in many cases can bypass the need for expensive numerical
simulations.Comment: 48 pages 14 figures RevTe
Dual Monte Carlo and Cluster Algorithms
We discuss the development of cluster algorithms from the viewpoint of
probability theory and not from the usual viewpoint of a particular model. By
using the perspective of probability theory, we detail the nature of a cluster
algorithm, make explicit the assumptions embodied in all clusters of which we
are aware, and define the construction of free cluster algorithms. We also
illustrate these procedures by rederiving the Swendsen-Wang algorithm,
presenting the details of the loop algorithm for a worldline simulation of a
quantum 1/2 model, and proposing a free cluster version of the
Swendsen-Wang replica method for the random Ising model. How the principle of
maximum entropy might be used to aid the construction of cluster algorithms is
also discussed.Comment: 25 pages, 4 figures, to appear in Phys.Rev.
- …