Series studies of the Potts model. I: The simple cubic Ising model

The finite lattice method of series expansion is generalised to the $q$-state Potts model on the simple cubic lattice. It is found that the computational effort grows exponentially with the square of the number of series terms obtained, unlike two-dimensional lattices where the computational requirements grow exponentially with the number of terms. For the Ising ($q=2$) case we have extended low-temperature series for the partition functions, magnetisation and zero-field susceptibility to $u^{26}$ from $u^{20}$. The high-temperature series for the zero-field partition function is extended from $v^{18}$ to $v^{22}$. Subsequent analysis gives critical exponents in agreement with those from field theory.Comment: submitted to J. Phys. A: Math. Gen. Uses preprint.sty: included. 24 page

Surface width of the Solid-On-Solid models

The low-temperature series for the surface width of the Absolute value Solid-On-Solid model and the Discrete Gaussian model both on the square lattice and on the triangular lattice are generated to high orders using the improved finite-lattice method. The series are analyzed to give the critical points of the roughening phase transition for each model.Comment: 3 pages, LaTeX, to appear in the proceedings of Lattice'97, Edinburgh, Scotland, July 22--26, 199

Low-Temperature Series for Ising Model by Finite-Lattice Method

We have calculated the low-temperature series for the second moment of the correlation function in $d=3$ Ising model to order $u^{26}$ and for the free energy of Absolute Value Solid-on-Solid (ASOS) model to order $u^{23}$, using the finite-lattice method.Comment: 3pages, latex, no figures, talk given at LATTICE'94, to appear in the proceeding

New algorithm of the high-temperature expansion for the Ising model in three dimensions

New algorithm of the finite lattice method is presented to generate the high-temperature expansion series of the Ising model. It enables us to obtain much longer series in three dimensions when compared not only to the previous algorithm of the finite lattice method but also to the standard graphical method. It is applied to extend the high-temperature series of the simple cubic Ising model from beta^{26} to beta^{46} for the free energy and from beta^{25} to beta^{32} for the magnetic susceptibility.Comment: 3 pages, Lattice2002(spin

The Pig Farm Manager for Modelling Pig Production Systems

Before setting up or changing a pig farm operation, the consequences of the farm set up must be explored and changes planned. To calculate technical and economic consequences a farm manager model for pig production systems, the Pig Farm Manager, has been developed. The Pig Farm Manager estimates the effects of various farm designs as well as farm management on production, environmental and economical parameters. The Pig Farm Manager includes simulations for sow farms and finisher pig farms. In the model the user enters farm data on e.g. farm size, housing system or farm management (e.g. feeding strategy), which the model uses to calculate output-parameters. The Pig Farm Manager estimates cost price, profits, gross margins, costs and income per farm, per sow or finisher place. To evaluate the analytical capacities of the model a comparison between a standard sow farm and a high-health-status farm was made. The high-health-farm (HHF) had better growth of piglets, lower mortality rate and better fertility traits for sows compared to a standard farm. However, the HHF had higher investment costs and required more labour. Overall, on the HHF, cost price per piglet was 3.19 lower and yearly farm income about 21,000,- higher compared to the standard sow farm.Livestock Production/Industries,

Higher orders of the high-temperature expansion for the Ising model in three dimensions

The new algorithm of the finite lattice method is applied to generate the high-temperature expansion series of the simple cubic Ising model to $\beta^{50}$ for the free energy, to $\beta^{32}$ for the magnetic susceptibility and to $\beta^{29}$ for the second moment correlation length. The series are analyzed to give the precise value of the critical point and the critical exponents of the model.Comment: Lattice2003(Higgs), 3 pages, 2 figure

Effect of slatted and solid floors and permeability of floors in pig houses on environment, animal welfare and health and food safety: a review of literature

An integrated approach can improve understanding of floor performance. Not only gap width or percentage of slatted floor is important, but a minimum percentage of permeability of the total floor area appears to be decisiv

High-temperature expansion of the magnetic susceptibility and higher moments of the correlation function for the two-dimensional XY model

We calculate the high-temperature series of the magnetic susceptibility and the second and fourth moments of the correlation function for the XY model on the square lattice to order $\beta^{33}$ by applying the improved algorithm of the finite lattice method. The long series allow us to estimate the inverse critical temperature as $\beta_c=1.1200(1)$, which is consistent with the most precise value given previously by the Monte Carlo simulation. The critical exponent for the multiplicative logarithmic correction is evaluated to be $\theta=0.054(10)$, which is consistent with the renormalization group prediction of $\theta={1/16}$.Comment: 13 pages, 8 Postscript figure

Large-q expansion of the energy and magnetization cumulants for the two-dimensional q-state Potts model

We have calculated the large-q expansion for the energy cumulants and the magnetization cumulants at the phase transition point in the two-dimensional q-state Potts model to the 21st or 23rd order in $1/\sqrt{q}$ using the finite lattice method. The obtained series allow us to give very precise estimates of the cumulants for $q>4$ on the first order transition point. The result confirms us the correctness of the conjecture by Bhattacharya et al. on the asymptotic behavior not only of the energy cumulants but also of the magnetization cumulants for $q \to 4_+$.Comment: 36 pages, LaTeX, 20 postscript figures, to appear in Nuclear Physics