311 research outputs found
Tumbling of a rigid rod in a shear flow
The tumbling of a rigid rod in a shear flow is analyzed in the high viscosity
limit. Following Burgers, the Master Equation is derived for the probability
distribution of the orientation of the rod. The equation contains one
dimensionless number, the Weissenberg number, which is the ratio of the shear
rate and the orientational diffusion constant. The equation is solved for the
stationary state distribution for arbitrary Weissenberg numbers, in particular
for the limit of high Weissenberg numbers. The stationary state gives an
interesting flow pattern for the orientation of the rod, showing the interplay
between flow due to the driving shear force and diffusion due to the random
thermal forces of the fluid. The average tumbling time and tumbling frequency
are calculated as a function of the Weissenberg number. A simple cross-over
function is proposed which covers the whole regime from small to large
Weissenberg numbers.Comment: 22 pages, 9 figure
Scaling in the vicinity of the four-state Potts fixed point
We study a self-dual generalization of the Baxter-Wu model, employing results
obtained by transfer matrix calculations of the magnetic scaling dimension and
the free energy. While the pure critical Baxter-Wu model displays the critical
behavior of the four-state Potts fixed point in two dimensions, in the sense
that logarithmic corrections are absent, the introduction of different
couplings in the up- and down triangles moves the model away from this fixed
point, so that logarithmic corrections appear. Real couplings move the model
into the first-order range, away from the behavior displayed by the
nearest-neighbor, four-state Potts model. We also use complex couplings, which
bring the model in the opposite direction characterized by the same type of
logarithmic corrections as present in the four-state Potts model. Our
finite-size analysis confirms in detail the existing renormalization theory
describing the immediate vicinity of the four-state Potts fixed point.Comment: 19 pages, 7 figure
d=2 transverse-field Ising model under the screw-boundary condition: An optimization of the screw pitch
A length-N spin chain with the \sqrt{N}(=v)-th neighbor interaction is
identical to a two-dimensional (d=2) model under the screw-boundary (SB)
condition. The SB condition provides a flexible scheme to construct a d\ge2
cluster from an arbitrary number of spins; the numerical diagonalization
combined with the SB condition admits a potential applicability to a class of
systems intractable with the quantum Monte Carlo method due to the
negative-sign problem. However, the simulation results suffer from
characteristic finite-size corrections inherent in SB. In order to suppress
these corrections, we adjust the screw pitch v(N) so as to minimize the
excitation gap for each N. This idea is adapted to the transverse-field Ising
model on the triangular lattice with N\le32 spins. As a demonstration, the
correlation-length critical exponent is analyzed in some detail
Monte Carlo Renormalization of the 3-D Ising model: Analyticity and Convergence
We review the assumptions on which the Monte Carlo renormalization technique
is based, in particular the analyticity of the block spin transformations. On
this basis, we select an optimized Kadanoff blocking rule in combination with
the simulation of a d=3 Ising model with reduced corrections to scaling. This
is achieved by including interactions with second and third neighbors. As a
consequence of the improved analyticity properties, this Monte Carlo
renormalization method yields a fast convergence and a high accuracy. The
results for the critical exponents are y_H=2.481(1) and y_T=1.585(3).Comment: RevTeX, 4 PostScript file
Field-induced Ordering in Critical Antiferromagnets
Transfer-matrix scaling methods have been used to study critical properties
of field-induced phase transitions of two distinct two-dimensional
antiferromagnets with discrete-symmetry order parameters: triangular-lattice
Ising systems (TIAF) and the square-lattice three-state Potts model (SPAF-3).
Our main findings are summarised as follows. For TIAF, we have shown that the
critical line leaves the zero-temperature, zero -field fixed point at a finite
angle. Our best estimate of the slope at the origin is . For SPAF-3 we provided evidence that the zero-field correlation
length diverges as , with , through analysis of the critical curve at plus crossover
arguments. For SPAF-3 we have also ascertained that the conformal anomaly and
decay-of-correlations exponent behave as: (a) H=0: ; (b) .Comment: RevTex, 7 pages, 4 eps figures, to be published in Phys. Rev.
On locations and properties of the multicritical point of Gaussian and +/-J Ising spin glasses
We use transfer-matrix and finite-size scaling methods to investigate the
location and properties of the multicritical point of two-dimensional Ising
spin glasses on square, triangular and honeycomb lattices, with both binary and
Gaussian disorder distributions. For square and triangular lattices with binary
disorder, the estimated position of the multicritical point is in numerical
agreement with recent conjectures regarding its exact location. For the
remaining four cases, our results indicate disagreement with the respective
versions of the conjecture, though by very small amounts, never exceeding 0.2%.
Our results for: (i) the correlation-length exponent governing the
ferro-paramagnetic transition; (ii) the critical domain-wall energy amplitude
; (iii) the conformal anomaly ; (iv) the finite-size susceptibility
exponent ; and (v) the set of multifractal exponents
associated to the moments of the probability distribution of spin-spin
correlation functions at the multicritical point, are consistent with
universality as regards lattice structure and disorder distribution, and in
good agreement with existing estimates.Comment: RevTeX 4, 9 pages, 2 .eps figure
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)
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