172 research outputs found
Dynamic critical behavior of the classical anisotropic BCC Heisenberg antiferromagnet
Using a recently implemented integration method [Krech et. al.] based on an
iterative second-order Suzuki-Trotter decomposition scheme, we have performed
spin dynamics simulations to study the critical dynamics of the BCC Heisenberg
antiferromagnet with uniaxial anisotropy. This technique allowed us to probe
the narrow asymptotic critical region of the model and estimate the dynamic
critical exponent . Comparisons with competing theories and
experimental results are presented.Comment: Latex, 3 pages, 5 figure
Convergence and Refinement of the Wang-Landau Algorithm
Recently, Wang and Landau proposed a new random walk algorithm that can be
very efficiently applied to many problems. Subsequently, there has been
numerous studies on the algorithm itself and many proposals for improvements
were put forward. However, fundamental questions such as what determines the
rate of convergence has not been answered. To understand the mechanism behind
the Wang-Landau method, we did an error analysis and found that a steady state
is reached where the fluctuations in the accumulated energy histogram saturate
at values proportional to . This value is closely related to
the error corrections to the Wang-Landau method. We also study the rate of
convergence using different "tuning" parameters in the algorithm.Comment: 6 pages, submitted to Comp. Phys. Com
Nature of the vortex-glass order in strongly type-II superconductors
The stability and the critical properties of the three-dimensional
vortex-glass order in random type-II superconductors with point disorder is
investigated in the unscreened limit based on a lattice {\it XY} model with a
uniform field. By performing equilibrium Monte Carlo simulations for the system
with periodic boundary conditions, the existence of a stable vortex-glass order
is established in the unscreened limit. Estimated critical exponents are
compared with those of the gauge-glass model.Comment: Error in the reported value of the exponent eta is correcte
Fast spin dynamics algorithms for classical spin systems
We have proposed new algorithms for the numerical integration of the
equations of motion for classical spin systems. In close analogy to symplectic
integrators for Hamiltonian equations of motion used in Molecular Dynamics
these algorithms are based on the Suzuki-Trotter decomposition of exponential
operators and unlike more commonly used algorithms exactly conserve spin length
and, in special cases, energy. Using higher order decompositions we investigate
integration schemes of up to fourth order and compare them to a well
established fourth order predictor-corrector method. We demonstrate that these
methods can be used with much larger time steps than the predictor-corrector
method and thus may lead to a substantial speedup of computer simulations of
the dynamical behavior of magnetic materials.Comment: 9 pages RevTeX with 8 figure
Clifford algebras and universal sets of quantum gates
In this paper is shown an application of Clifford algebras to the
construction of computationally universal sets of quantum gates for -qubit
systems. It is based on the well-known application of Lie algebras together
with the especially simple commutation law for Clifford algebras, which states
that all basic elements either commute or anticommute.Comment: 4 pages, REVTeX (2 col.), low-level language corrections, PR
Hierarchical Mean-Field Theories in Quantum Statistical Mechanics
We present a theoretical framework and a calculational scheme to study the
coexistence and competition of thermodynamic phases in quantum statistical
mechanics. The crux of the method is the realization that the microscopic
Hamiltonian, modeling the system, can always be written in a hierarchical
operator language that unveils all symmetry generators of the problem and,
thus, possible thermodynamic phases. In general one cannot compute the
thermodynamic or zero-temperature properties exactly and an approximate scheme
named ``hierarchical mean-field approach'' is introduced. This approach treats
all possible competing orders on an equal footing. We illustrate the
methodology by determining the phase diagram and quantum critical point of a
bosonic lattice model which displays coexistence and competition between
antiferromagnetism and superfluidity.Comment: 4 pages, 2 psfigures. submitted Phys. Rev.
Dynamic Critical Behavior of the Heisenberg Model with Strong Easy Plane Anisotropy
The dynamic critical behavior of the Heisenberg model with a strong
anisotropy of the exchange constant in the z direction is investigated. The
main features of the time evolution of this model are revealed. The static and
dynamic critical behavior of planar magnetic models is shown to be described
well by the Heisenberg model with strong easy plane anisotropy.Comment: 5 pages, 4 figures, 1 tabl
Phase Transitions of Hard Disks in External Periodic Potentials: A Monte Carlo Study
The nature of freezing and melting transitions for a system of hard disks in
a spatially periodic external potential is studied using extensive Monte Carlo
simulations. Detailed finite size scaling analysis of various thermodynamic
quantities like the order parameter, its cumulants etc. are used to map the
phase diagram of the system for various values of the density and the amplitude
of the external potential. We find clear indication of a re-entrant liquid
phase over a significant region of the parameter space. Our simulations
therefore show that the system of hard disks behaves in a fashion similar to
charge stabilized colloids which are known to undergo an initial freezing,
followed by a re-melting transition as the amplitude of the imposed, modulating
field produced by crossed laser beams is steadily increased. Detailed analysis
of our data shows several features consistent with a recent dislocation
unbinding theory of laser induced melting.Comment: 36 pages, 16 figure
Shift in critical temperature for random spatial permutations with cycle weights
We examine a phase transition in a model of random spatial permutations which
originates in a study of the interacting Bose gas. Permutations are weighted
according to point positions; the low-temperature onset of the appearance of
arbitrarily long cycles is connected to the phase transition of Bose-Einstein
condensates. In our simplified model, point positions are held fixed on the
fully occupied cubic lattice and interactions are expressed as Ewens-type
weights on cycle lengths of permutations. The critical temperature of the
transition to long cycles depends on an interaction-strength parameter
. For weak interactions, the shift in critical temperature is expected
to be linear in with constant of linearity . Using Markov chain
Monte Carlo methods and finite-size scaling, we find .
This finding matches a similar analytical result of Ueltschi and Betz. We also
examine the mean longest cycle length as a fraction of the number of sites in
long cycles, recovering an earlier result of Shepp and Lloyd for non-spatial
permutations.Comment: v2 incorporated reviewer comments. v3 removed two extraneous figures
which appeared at the end of the PDF
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