4,695 research outputs found

### Numerical Latent Heat Observation of the q=5 Potts Model

Site energy of the five-state ferromagnetic Potts model is numerically
calculated at the first-order transition temperature using corner transfer
matrix renormalization group (CTMRG) method. The calculated energy of the
disordered phase $U^{+}$ is clearly different from that of the ordered phase
$U^{-}$. The obtained latent heat $L = U^{-} - U^{+}$ is 0.027, which
quantitatively agrees with the exact solution.Comment: 2 pages, Latex(JPSJ style files are included), 2 ps figures,
submitted to J. Phys. Soc. Jpn.(short note

### The Density Matrix Renormalization Group technique with periodic boundary conditions

The Density Matrix Renormalization Group (DMRG) method with periodic boundary
conditions is introduced for two dimensional classical spin models. It is shown
that this method is more suitable for derivation of the properties of infinite
2D systems than the DMRG with open boundary conditions despite the latter
describes much better strips of finite width. For calculation at criticality,
phenomenological renormalization at finite strips is used together with a
criterion for optimum strip width for a given order of approximation. For this
width the critical temperature of 2D Ising model is estimated with seven-digit
accuracy for not too large order of approximation. Similar precision is reached
for critical indices. These results exceed the accuracy of similar calculations
for DMRG with open boundary conditions by several orders of magnitude.Comment: REVTeX format contains 8 pages and 6 figures, submitted to Phys. Rev.

### Stochastic Light-Cone CTMRG: a new DMRG approach to stochastic models

We develop a new variant of the recently introduced stochastic
transfer-matrix DMRG which we call stochastic light-cone corner-transfer-matrix
DMRG (LCTMRG). It is a numerical method to compute dynamic properties of
one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a
modification of the corner-transfer-matrix DMRG (CTMRG), adjusted by an
additional causality argument. As an example, two reaction-diffusion models,
the diffusion-annihilation process and the branch-fusion process, are studied
and compared to exact data and Monte-Carlo simulations to estimate the
capability and accuracy of the new method. The number of possible Trotter steps
of more than 10^5 shows a considerable improvement to the old stochastic TMRG
algorithm.Comment: 15 pages, uses IOP styl

### Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix Renormalization Group

We report a way of obtaining a spin configuration snapshot, which is one of
the representative spin configurations in canonical ensemble, in a finite area
of infinite size two-dimensional (2D) classical lattice models. The corner
transfer matrix renormalization group (CTMRG), a variant of the density matrix
renormalization group (DMRG), is used for the numerical calculation. The matrix
product structure of the variational state in CTMRG makes it possible to
stochastically fix spins each by each according to the conditional probability
with respect to its environment.Comment: 4 pages, 8figure

### Performance of an ideal turbine in an inviscid shear flow

Although wind and tidal turbines operate in turbulent shear flow, most theoretical results concerning turbine performance, such as the well-known Betz limit, assume the upstream velocity profile is uniform. To improve on these existing results we extend the classical actuator disc model in this paper to investigate the performance of an ideal turbine in steady, inviscid shear flow. The model is developed on the assumption that there is negligible lateral interaction in the flow passing through the disc and that the actuator applies a uniform resistance across its area. With these assumptions, solution of the model leads to two key results. First, for laterally unbounded shear flow, it is shown that the normalised power extracted is the same as that for an ideal turbine in uniform flow, if the average of the cube of the upstream velocity of the fluid passing through the turbine is used in the normalisation. Second, for a laterally bounded shear flow, it is shown that the same normalisation can be applied, but allowance must also be made for the fact that non-uniform flow bypassing the turbine alters the background pressure gradient and, in turn, the turbines â€˜effective blockageâ€™ (so that it may be greater or less than the geometric blockage, defined as the ratio of turbine disc area to cross-sectional area of the flow). Predictions based on the extended model agree well with numerical simulations approximating the incompressible Euler equations. The model may be used to improve interpretation of model-scale results for wind and tidal turbines in tunnels/flumes, to investigate the variation in force across a turbine and to update existing theoretical models of arrays of tidal turbines

### Incommensurate structures studied by a modified Density Matrix Renormalization Group Method

A modified density matrix renormalization group (DMRG) method is introduced
and applied to classical two-dimensional models: the anisotropic triangular
nearest- neighbor Ising (ATNNI) model and the anisotropic triangular
next-nearest-neighbor Ising (ANNNI) model. Phase diagrams of both models have
complex structures and exhibit incommensurate phases. It was found that the
incommensurate phase completely separates the disordered phase from one of the
commensurate phases, i. e. the non-existence of the Lifshitz point in phase
diagrams of both models was confirmed.Comment: 14 pages, 14 figures included in text, LaTeX2e, submitted to PRB,
presented at MECO'24 1999 (Wittenberg, Germany

### Flat-Bands on Partial Line Graphs -- Systematic Method for Generating Flat-Band Lattice Structures

We introduce a systematic method for constructing a class of lattice
structures that we call ``partial line graphs''.In tight-binding models on
partial line graphs, energy bands with flat energy dispersions emerge.This
method can be applied to two- and three-dimensional systems. We show examples
of partial line graphs of square and cubic lattices. The method is useful in
providing a guideline for synthesizing materials with flat energy bands, since
the tight-binding models on the partial line graphs provide us a large room for
modification, maintaining the flat energy dispersions.Comment: 9 pages, 4 figure

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