2,689 research outputs found
New critical frontiers for the Potts and percolation models
We obtain the critical threshold for a host of Potts and percolation models
on lattices having a structure which permits a duality consideration. The
consideration generalizes the recently obtained thresholds of Scullard and Ziff
for bond and site percolation on the martini and related lattices to the Potts
model and to other lattices.Comment: 9 pages, 5 figure
Internal Energy of the Potts model on the Triangular Lattice with Two- and Three-body Interactions
We calculate the internal energy of the Potts model on the triangular lattice
with two- and three-body interactions at the transition point satisfying
certain conditions for coupling constants. The method is a duality
transformation. Therefore we have to make assumptions on uniqueness of the
transition point and that the transition is of second order. These assumptions
have been verified to hold by numerical simulations for q=2, 3 and 4, and our
results for the internal energy are expected to be exact in these cases.Comment: 9 pages, 4 figure
On the duality relation for correlation functions of the Potts model
We prove a recent conjecture on the duality relation for correlation
functions of the Potts model for boundary spins of a planar lattice.
Specifically, we deduce the explicit expression for the duality of the n-site
correlation functions, and establish sum rule identities in the form of the
M\"obius inversion of a partially ordered set. The strategy of the proof is by
first formulating the problem for the more general chiral Potts model. The
extension of our consideration to the many-component Potts models is also
given.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.
Integrability of the critical point of the Kagom\'e three-state Potts mode
The vicinity of the critical point of the three-state Potts model on a
Kagom\'e lattice is studied by mean of Random Matrix Theory. Strong evidence
that the critical point is integrable is given.Comment: 1 LaTex file + 3 eps files 7 page
Canola and mustard response to short periods of high temperature and drought stresses at different growth stages
Non-Peer ReviewedBrassica crops grown on the semiarid Canadian prairie are often subject to heat and water stress during the period of flowering. A growth chamber study was conducted at Swift Current to understand the effects of short periods of high temperature stress and/or water stress at different developmental stages on the seed yield formation of different Brassica species. Two advanced breeding lines of canola quality Brassica juncea (PC98-44 and PC98-45) along with a canola cv. Quantum (B. napus L.) and a mustard cv. Cutlass (B.
juncea L.) were grown under 20/18 °C day/night temperature. High (35/18 °C) and low (28/18 °C) temperature stresses were imposed for 10 days at bolting, flowering or pod formation stages in two separate growth cabinets. At the same time, low (90% available water) or high (50% available water) water stress was imposed on half of the plants in each of the temperature treatments. All yield components were affected by temperature stress, while water stress had no effect on most yield components. The severe reduction of pods main shoot-1 (75%), seeds pod-1 (25%), and seed weight (22%) by 35/18 °C, reduced main stem seed yield of by 87% in all Brassica cultivars. However, seed yield reduction per plant by the same stress was 51%, indicating recovery from the stress treatments by Brassica species. Delaying exposure to stress to pod development stage reduced the chance of the plant to recover from the stress. The low water stress was to encouraging better recovery at 28/18 °C stress. In the controlled growth chamber, B. juncea cultivars responded to heat stress by increasing pod production but ignoring filling
pods, while B. napus maintained a better seed fill. Under field conditions where plant-to-plant competition is strong, B. juncea may produce more pods with higher seed yield than canola; this needs to be confirmed with further field trials
On the origin of multiple ordered phases in PrFe4P12
The nature of multiple electronic orders in skutterudite PrFe_4P_{12} is
discussed on the basis of a model with antiferro-quadrupole (AFQ) interaction
of \Gamma_3 symmetry. The high-field phase can be reproduced qualitatively
provided (i) ferro-type interactions are introduced between the dipoles as well
as between the octupoles of localized f-electrons, and (ii) separation is
vanishingly small between the \Gamma_1-\Gamma_4^{(1)} crystalline electric
field (CEF) levels. The high-field phase can have either the same ordering
vector q=(1,0,0) as in the low-field phase, or a different one q=0 depending on
the parameters. In the latter case, distortion of the crystal perpendicular to
the (111) axis is predicted. The corresponding anomaly in elastic constants
should also appear. The electrical resistivity is calculated with account of
scattering within the CEF quasi-quartet. It is found that the resistivity as a
function of the direction of magnetic field shows a sharp maximum around the
(111) axis at low temperatures because of the level crossing.Comment: 16 pages, 5 figure
Probability-Changing Cluster Algorithm: Study of Three-Dimensional Ising Model and Percolation Problem
We present a detailed description of the idea and procedure for the newly
proposed Monte Carlo algorithm of tuning the critical point automatically,
which is called the probability-changing cluster (PCC) algorithm [Y. Tomita and
Y. Okabe, Phys. Rev. Lett. {\bf 86} (2001) 572]. Using the PCC algorithm, we
investigate the three-dimensional Ising model and the bond percolation problem.
We employ a refined finite-size scaling analysis to make estimates of critical
point and exponents. With much less efforts, we obtain the results which are
consistent with the previous calculations. We argue several directions for the
application of the PCC algorithm.Comment: 6 pages including 8 eps figures, to appear in J. Phys. Soc. Jp
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 is clearly different from that of the ordered phase
. The obtained latent heat 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
Analogues of Kahan's method for higher order equations of higher degree
Kahan introduced an explicit method of discretization for systems of first order differential equations with nonlinearities of degree at most two (quadratic vector fields). Kahan's method has attracted much interest due to the fact that it preserves many of the geometrical properties of the original continuous system. In particular, a large number of Hamiltonian systems of quadratic vector fields are known for which their Kahan discretization is a discrete integrable system. In this note, we introduce a special class of explicit order-preserving discretization schemes that are appropriate for certain systems of ordinary differential equations of higher order and higher degree
Monte Carlo Study of an Extended 3-State Potts Model on the Triangular Lattice
By introducing a chiral term into the Hamiltonian of the 3-state Potts model
on a triangular lattice additional symmetries are achieved between the
clockwise and anticlockwise states and the ferromagnetic state. This model is
investigated using Monte Carlo methods. We investigate the full phase diagram
and find evidence for a line tricritical points separating the ferromagnetic
and antiferromagnetic phases.Comment: 6 pages, 10 figure
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