2,794 research outputs found
Improved Phenomenological Renormalization Schemes
An analysis is made of various methods of phenomenological renormalization
based on finite-size scaling equations for inverse correlation lengths, the
singular part of the free energy density, and their derivatives. The analysis
is made using two-dimensional Ising and Potts lattices and the
three-dimensional Ising model. Variants of equations for the phenomenological
renormalization group are obtained which ensure more rapid convergence than the
conventionally used Nightingale phenomenological renormalization scheme. An
estimate is obtained for the critical finite-size scaling amplitude of the
internal energy in the three-dimensional Ising model. It is shown that the
two-dimensional Ising and Potts models contain no finite-size corrections to
the internal energy so that the positions of the critical points for these
models can be determined exactly from solutions for strips of finite width. It
is also found that for the two-dimensional Ising model the scaling finite-size
equation for the derivative of the inverse correlation length with respect to
temperature gives the exact value of the thermal critical exponent.Comment: 14 pages with 1 figure in late
Computation of Dominant Eigenvalues and Eigenvectors: A Comparative Study of Algorithms
We investigate two widely used recursive algorithms for the computation of eigenvectors with extreme eigenvalues of large symmetric matrices -- the modified Lanczös method and the conjugate-gradient method. The goal is to establish a connection between their underlying principles and to evaluate their performance in applications to Hamiltonian and transfer matrices of selected model systems of interest in condensed matter physics and statistical mechanics. The conjugate-gradient method is found to converge more rapidly for understandable reasons, while storage requirements are the same for both methods
Critical temperature of a fully anisotropic three-dimensional Ising model
The critical temperature of a three-dimensional Ising model on a simple cubic
lattice with different coupling strengths along all three spatial directions is
calculated via the transfer matrix method and a finite size scaling for L x L
oo clusters (L=2 and 3). The results obtained are compared with available
calculations. An exact analytical solution is found for the 2 x 2 oo Ising
chain with fully anisotropic interactions (arbitrary J_x, J_y and J_z).Comment: 17 pages in tex using preprint.sty for IOP journals, no figure
Conformal Anomaly and Critical Exponents of the XY-Ising Model
We use extensive Monte Carlo transfer matrix calculations on infinite strips
of widths up to 30 lattice spacing and a finite-size scaling analysis to
obtain critical exponents and conformal anomaly number for the
two-dimensional -Ising model. This model is expected to describe the
critical behavior of a class of systems with simultaneous and
symmetries of which the fully frustrated model is a special case. The
effective values obtained for show a significant decrease with at
different points along the line where the transition to the ordered phase takes
place in a single transition. Extrapolations based on power-law corrections
give values consistent with although larger values can not be ruled
out. Critical exponents are obtained more accurately and are consistent with
previous Monte Carlo simulations suggesting new critical behavior and with
recent calculations for the frustrated model.Comment: 33 pages, 13 latex figures, uses RevTeX 3.
Screen time is associated with adiposity and insulin resistance in children
Higher screen time is associated with type 2 diabetes (T2D) risk in adults, but the association with T2D risk markers in children is unclear. We examined associations between self-reported screen time and T2D risk markers in children. Survey of 4495 children aged 9-10 years who had fasting cardiometabolic risk marker assessments, anthropometry measurements and reported daily screen time; objective physical activity was measured in a subset of 2031 children. Compared with an hour or less screen time daily, those reporting screen time over 3 hours had higher ponderal index (1.9%, 95% CI 0.5% to 3.4%), skinfold thickness (4.5%, 0.2% to 8.8%), fat mass index (3.3%, 0.0% to 6.7%), leptin (9.2%, 1.1% to 18.0%) and insulin resistance (10.5%, 4.9% to 16.4%); associations with glucose, HbA1c, physical activity and cardiovascular risk markers were weak or absent. Associations with insulin resistance remained after adjustment for adiposity, socioeconomic markers and physical activity. Strong graded associations between screen time, adiposity and insulin resistance suggest that reducing screen time could facilitate early T2D prevention. While these observations are of considerable public health interest, evidence from randomised controlled trials is needed to suggest causality. [Abstract copyright: Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/.
High-precision estimate of g4 in the 2D Ising model
We compute the renormalized four-point coupling in the 2d Ising model using
transfer-matrix techniques. We greatly reduce the systematic uncertainties
which usually affect this type of calculations by using the exact knowledge of
several terms in the scaling function of the free energy. Our final result is
g4=14.69735(3).Comment: 17 pages, revised version with minor changes, accepted for
publication in Journal of Physics
The Dynamic Exponent of the Two-Dimensional Ising Model and Monte Carlo Computation of the Sub-Dominant Eigenvalue of the Stochastic Matrix
We introduce a novel variance-reducing Monte Carlo algorithm for accurate
determination of autocorrelation times. We apply this method to two-dimensional
Ising systems with sizes up to , using single-spin flip dynamics,
random site selection and transition probabilities according to the heat-bath
method. From a finite-size scaling analysis of these autocorrelation times, the
dynamical critical exponent is determined as (12)
The phase diagram of the anisotropic Spin-1 Heisenberg Chain
We applied the Density Matrix Renormalization Group to the XXZ spin-1 quantum
chain. In studing this model we aim to clarify controversials about the point
where the massive Haldane phase appears.Comment: 2 pages (standart LaTex), 1 figure (PostScript) uuencode
Quantum Speedup by Quantum Annealing
We study the glued-trees problem of Childs et. al. in the adiabatic model of
quantum computing and provide an annealing schedule to solve an oracular
problem exponentially faster than classically possible. The Hamiltonians
involved in the quantum annealing do not suffer from the so-called sign
problem. Unlike the typical scenario, our schedule is efficient even though the
minimum energy gap of the Hamiltonians is exponentially small in the problem
size. We discuss generalizations based on initial-state randomization to avoid
some slowdowns in adiabatic quantum computing due to small gaps.Comment: 7 page
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