1,033 research outputs found
Thermodynamics of the Antiferromagnetic Heisenberg Model on the Checkerboard Lattice
Employing numerical linked-cluster expansions (NLCEs) along with exact
diagonalizations of finite clusters with periodic boundary condition, we study
the energy, specific heat, entropy, and various susceptibilities of the
antiferromagnetic Heisenberg model on the checkerboard lattice. NLCEs, combined
with extrapolation techniques, allow us to access temperatures much lower than
those accessible to exact diagonalization and other series expansions. We find
that the high-temperature peak in specific heat decreases as the frustration
increases, consistent with the large amount of unquenched entropy in the region
around maximum classical frustration, where the nearest-neighbor and
next-nearest neighbor exchange interactions (J and J', respectively) have the
same strength, and with the formation of a second peak at lower temperatures.
The staggered susceptibility shows a change of character when J' increases
beyond 0.75J, implying the disappearance of the long-range antiferromagnetic
order at zero temperature. For J'=4J, in the limit of weakly coupled crossed
chains, we find large susceptibilities for stripe and Neel order with
Q=(pi/2,pi/2) at low temperatures with antiferromagnetic correlations along the
chains. Other magnetic and bond orderings, such as a plaquette valence-bond
solid and a crossed-dimer order suggested by previous studies, have also been
investigated.Comment: 10 pages, 13 figure
Directed percolation near a wall
Series expansion methods are used to study directed bond percolation clusters
on the square lattice whose lateral growth is restricted by a wall parallel to
the growth direction. The percolation threshold is found to be the same
as that for the bulk. However the values of the critical exponents for the
percolation probability and mean cluster size are quite different from those
for the bulk and are estimated by and respectively. On the other hand the exponent
characterising the scale of the cluster size
distribution is found to be unchanged by the presence of the wall.
The parallel connectedness length, which is the scale for the cluster length
distribution, has an exponent which we estimate to be and is also unchanged. The exponent of the mean
cluster length is related to and by the scaling
relation and using the above estimates
yields to within the accuracy of our results. We conjecture that
this value of is exact and further support for the conjecture is
provided by the direct series expansion estimate .Comment: 12pages LaTeX, ioplppt.sty, to appear in J. Phys.
Critical behaviour of the two-dimensional Ising susceptibility
We report computations of the short-distance and the long-distance (scaling)
contributions to the square-lattice Ising susceptibility in zero field close to
T_c. Both computations rely on the use of nonlinear partial difference
equations for the correlation functions. By summing the correlation functions,
we give an algorithm of complexity O(N^6) for the determination of the first N
series coefficients. Consequently, we have generated and analysed series of
length several hundred terms, generated in about 100 hours on an obsolete
workstation. In terms of a temperature variable, \tau, linear in T/T_c-1, the
short-distance terms are shown to have the form \tau^p(ln|\tau|)^q with p>=q^2.
To O(\tau^14) the long-distance part divided by the leading \tau^{-7/4}
singularity contains only integer powers of \tau. The presence of irrelevant
variables in the scaling function is clearly evident, with contributions of
distinct character at leading orders |\tau|^{9/4} and |\tau|^{17/4} being
identified.Comment: 11 pages, REVTex
Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices
We discuss recently introduced numerical linked-cluster (NLC) algorithms that
allow one to obtain temperature-dependent properties of quantum lattice models,
in the thermodynamic limit, from exact diagonalization of finite clusters. We
present studies of thermodynamic observables for spin models on square,
triangular, and kagome lattices. Results for several choices of clusters and
extrapolations methods, that accelerate the convergence of NLC, are presented.
We also include a comparison of NLC results with those obtained from exact
analytical expressions (where available), high-temperature expansions (HTE),
exact diagonalization (ED) of finite periodic systems, and quantum Monte Carlo
simulations.For many models and properties NLC results are substantially more
accurate than HTE and ED.Comment: 14 pages, 16 figures, as publishe
Series expansions of the percolation probability on the directed triangular lattice
We have derived long series expansions of the percolation probability for
site, bond and site-bond percolation on the directed triangular lattice. For
the bond problem we have extended the series from order 12 to 51 and for the
site problem from order 12 to 35. For the site-bond problem, which has not been
studied before, we have derived the series to order 32. Our estimates of the
critical exponent are in full agreement with results for similar
problems on the square lattice, confirming expectations of universality. For
the critical probability and exponent we find in the site case: and ; in the bond case:
and ; and in the site-bond
case: and . In
addition we have obtained accurate estimates for the critical amplitudes. In
all cases we find that the leading correction to scaling term is analytic,
i.e., the confluent exponent .Comment: 26 pages, LaTeX. To appear in J. Phys.
Series Analysis of Tricritical Behavior: Mean-Field Model and Slicewise Pade Approximants
A mean-field model is proposed as a test case for tricritical series analyses
methods. Derivation of the 50th order series for the magnetization is reported.
As the first application this series is analyzed by the traditional slicewise
Pade approximant method popular in earlier studies of tricriticality.Comment: 22 pages in plain TeX; 7 PostScript figs available by e-mai
Information-theoretic determination of ponderomotive forces
From the equilibrium condition applied to an isolated
thermodynamic system of electrically charged particles and the fundamental
equation of thermodynamics () subject
to a new procedure, it is obtained the Lorentz's force together with
non-inertial terms of mechanical nature. Other well known ponderomotive forces,
like the Stern-Gerlach's force and a force term related to the Einstein-de
Haas's effect are also obtained. In addition, a new force term appears,
possibly related to a change in weight when a system of charged particles is
accelerated.Comment: 10 page
Complex-Temperature Singularities in the Ising Model. III. Honeycomb Lattice
We study complex-temperature properties of the uniform and staggered
susceptibilities and of the Ising model on the honeycomb
lattice. From an analysis of low-temperature series expansions, we find
evidence that and both have divergent singularities at the
point (where ), with exponents
. The critical amplitudes at this
singularity are calculated. Using exact results, we extract the behaviour of
the magnetisation and specific heat at complex-temperature
singularities. We find that, in addition to its zero at the physical critical
point, diverges at with exponent , vanishes
continuously at with exponent , and vanishes
discontinuously elsewhere along the boundary of the complex-temperature
ferromagnetic phase. diverges at with exponent
and at (where ) with exponent , and
diverges logarithmically at . We find that the exponent relation
is violated at ; the right-hand side is 4
rather than 2. The connections of these results with complex-temperature
properties of the Ising model on the triangular lattice are discussed.Comment: 22 pages, latex, figures appended after the end of the text as a
compressed, uuencoded postscript fil
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