22 research outputs found
New Algorithm of the Finite Lattice Method for the High-temperature Expansion of the Ising Model in Three Dimensions
We propose a new algorithm of the finite lattice method to generate the
high-temperature series for the Ising model in three dimensions. It enables us
to extend the series for the free energy of the simple cubic lattice from the
previous series of 26th order to 46th order in the inverse temperature. The
obtained series give the estimate of the critical exponent for the specific
heat in high precision.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Letter
Percolation and epidemics in a two-dimensional small world
Percolation on two-dimensional small-world networks has been proposed as a
model for the spread of plant diseases. In this paper we give an analytic
solution of this model using a combination of generating function methods and
high-order series expansion. Our solution gives accurate predictions for
quantities such as the position of the percolation threshold and the typical
size of disease outbreaks as a function of the density of "shortcuts" in the
small-world network. Our results agree with scaling hypotheses and numerical
simulations for the same model.Comment: 7 pages, 3 figures, 2 table
Planar lattice gases with nearest-neighbour exclusion
We discuss the hard-hexagon and hard-square problems, as well as the
corresponding problem on the honeycomb lattice. The case when the activity is
unity is of interest to combinatorialists, being the problem of counting binary
matrices with no two adjacent 1's. For this case we use the powerful corner
transfer matrix method to numerically evaluate the partition function per site,
density and some near-neighbour correlations to high accuracy. In particular
for the square lattice we obtain the partition function per site to 43 decimal
places.Comment: 16 pages, 2 built-in Latex figures, 4 table
Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial
We derive some new structural results for the transfer matrix of
square-lattice Potts models with free and cylindrical boundary conditions. In
particular, we obtain explicit closed-form expressions for the dominant (at
large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as
the solution of a special one-dimensional polymer model. We also obtain the
large-q expansion of the bulk and surface (resp. corner) free energies for the
zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47}
(resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <=
m <= 12 with free boundary conditions and locate roughly the limiting curves.Comment: 111 pages (LaTeX2e). Includes tex file, three sty files, and 19
Postscript figures. Also included are Mathematica files data_CYL.m and
data_FREE.m. Many changes from version 1: new material on series expansions
and their analysis, and several proofs of previously conjectured results.
Final version to be published in J. Stat. Phy
Transfer matrices and partition-function zeros for antiferromagnetic Potts models. VI. Square lattice with special boundary conditions
We study, using transfer-matrix methods, the partition-function zeros of the
square-lattice q-state Potts antiferromagnet at zero temperature (=
square-lattice chromatic polynomial) for the special boundary conditions that
are obtained from an m x n grid with free boundary conditions by adjoining one
new vertex adjacent to all the sites in the leftmost column and a second new
vertex adjacent to all the sites in the rightmost column. We provide numerical
evidence that the partition-function zeros are becoming dense everywhere in the
complex q-plane outside the limiting curve B_\infty(sq) for this model with
ordinary (e.g. free or cylindrical) boundary conditions. Despite this, the
infinite-volume free energy is perfectly analytic in this region.Comment: 114 pages (LaTeX2e). Includes tex file, three sty files, and 23
Postscript figures. Also included are Mathematica files data_Eq.m,
data_Neq.m,and data_Diff.m. Many changes from version 1, including several
proofs of previously conjectured results. Final version to be published in J.
Stat. Phy
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Carbon dioxide and climate impulse response functions for the computation of greenhouse gas metrics: A multi-model analysis
The responses of carbon dioxide (CO2) and other climate variables to an emission pulse of CO2 into the atmosphere are often used to compute the Global Warming Potential (GWP) and Global Temperature change Potential (GTP), to characterize the response timescales of Earth System models, and to build reduced-form models. In this carbon cycle-climate model intercomparison project, which spans the full model hierarchy, we quantify responses to emission pulses of different magnitudes injected under different conditions. The CO2 response shows the known rapid decline in the first few decades followed by a millennium-scale tail. For a 100 Gt-C emission pulse added to a constant CO2 concentration of 389 ppm, 25 ± 9% is still found in the atmosphere after 1000 yr; the ocean has absorbed 59 ± 12% and the land the remainder (16 ± 14%). The response in global mean surface air temperature is an increase by 0.20 ± 0.12 °C within the first twenty years; thereafter and until year 1000, temperature decreases only slightly, whereas ocean heat content and sea level continue to rise. Our best estimate for the Absolute Global Warming Potential, given by the time-integrated response in CO2 at year 100 multiplied by its radiative efficiency, is 92.5 × 10−15 yr W m−2 per kg-CO2. This value very likely (5 to 95% confidence) lies within the range of (68 to 117) × 10−15 yr W m−2 per kg-CO2. Estimates for time-integrated response in CO2 published in the IPCC First, Second, and Fourth Assessment and our multi-model best estimate all agree within 15% during the first 100 yr. The integrated CO2 response, normalized by the pulse size, is lower for pre-industrial conditions, compared to present day, and lower for smaller pulses than larger pulses. In contrast, the response in temperature, sea level and ocean heat content is less sensitive to these choices. Although, choices in pulse size, background concentration, and model lead to uncertainties, the most important and subjective choice to determine AGWP of CO2 and GWP is the time horizon
Offsetting methane emissions : an alternative to emission equivalence metrics
It is widely recognised that defining trade-offs between greenhouse gas emissions using ‘emission equivalence’ based on global warming potentials (GWPs) referenced to carbon dioxide produces anomalous results when applied to methane. The short atmospheric lifetime of methane, compared to the timescales of CO2 uptake, leads to the greenhouse warming depending strongly on the temporal pattern of emission substitution. We argue that a more appropriate way to consider the relationship between the warming effects of methane and carbon dioxide is to define a ‘mixed metric’ that compares ongoing methane emissions (or reductions) to one-off emissions (or reductions) of carbon dioxide. Quantifying this approach, we propose that a one-off sequestration of 1 t of carbon would offset an ongoing methane emission in the range 0.90–1.05 kg CH4 per year. We present an example of how our approach would apply to rangeland cattle production, and consider the broader context of mitigation of climate change, noting the reverse trade-off would raise significant challenges in managing the risk of non-compliance. Our analysis is consistent with other approaches to addressing the criticisms of GWP-based emission equivalence, but provides a simpler and more robust approach while still achieving close equivalence of climate mitigation outcomes ranging over decadal to multi-century timescales