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

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

Calculation of the work function with a local basis set

Electronic structure codes usually allow to calculate the work function as a part of the theoretical description of surfaces and processes such as adsorption thereon. This requires a proper calculation of the electrostatic potential in all regions of space, which is apparently straightforward to achieve with plane wave basis sets, but more difficult with local basis sets. To overcome this, a relatively simple scheme is proposed to accurately compute the work function when a local basis set is used, by having some additional basis functions in the vacuum. Tests on various surfaces demonstrate that a very good agreement with experimental and other theoretical data can be achieved.Comment: to appear in Surf. Sci. Let

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

Specific heat and high-temperature series of lattice models: interpolation scheme and examples on quantum spin systems in one and two dimensions

We have developed a new method for evaluating the specific heat of lattice spin systems. It is based on the knowledge of high-temperature series expansions, the total entropy of the system and the low-temperature expected behavior of the specific heat as well as the ground-state energy. By the choice of an appropriate variable (entropy as a function of energy), a stable interpolation scheme between low and high temperature is performed. Contrary to previous methods, the constraint that the total entropy is log(2S+1) for a spin S on each site is automatically satisfied. We present some applications to quantum spin models on one- and two- dimensional lattices. Remarkably, in most cases, a good accuracy is obtained down to zero temperature.Comment: 10 pages (RevTeX 4) including 11 eps figures. To appear in Phys. Rev.

Low temperature expansion for the 3-d Ising Model

We compute the weak coupling expansion for the energy of the three dimensional Ising model through 48 excited bonds. We also compute the magnetization through 40 excited bonds. This was achieved via a recursive enumeration of states of fixed energy on a set of finite lattices. We use a linear combination of lattices with a generalization of helical boundary conditions to eliminate finite volume effects.Comment: 10 pages, IASSNS-HEP-92/42, BNL-4767

Low-Temperature Series for the Correlation Length in d=3d=3 Ising Model

We extend low-temperature series for the second moment of the correlation function in $d=3$ simple-cubic Ising model from $u^{15}$ to $u^{26}$ using finite-lattice method, and combining with the series for the susceptibility we obtain the low-temperature series for the second-moment correlation length to $u^{23}$. An analysis of the obtained series by inhomogeneous differential approximants gives critical exponents $2\nu^{\prime} + \gamma^{\prime} \approx 2.55$ and $2\nu^{\prime} \approx 1.27$.Comment: 13 pages + 5 uuencoded epsf figures in Latex, OPCT-94-

Disentangling the effect of farming practice and aridity on crop stable isotope values: a present-day model from Morocco and its application to early farming sites in the eastern Mediterranean

Agriculture has played a pivotal role in shaping landscapes, soils and vegetation. Developing a better understanding of early farming practices can contribute to wider questions regarding the long-term impact of farming and its nature in comparison with present-day traditional agrosystems. In this study we determine stable carbon and nitrogen isotope values of barley grains from a series of present-day traditionally managed farming plots in Morocco, capturing a range of annual rainfall and farming practices. This allows a framework to be developed to refine current isotopic approaches used to infer manuring intensity and crop water status in (semi-)arid regions. This method has been applied to charred crop remains from two early farming sites in the eastern Mediterranean: Abu Hureyra and ‘Ain Ghazal. In this way, our study enhances knowledge of agricultural practice in the past, adding to understanding of how people have shaped and adapted to their environment over thousands of years

Kondo Effect in a Metal with Correlated Conduction Electrons: Diagrammatic Approach

We study the low-temperature behavior of a magnetic impurity which is weakly coupled to correlated conduction electrons. To account for conduction electron interactions a diagrammatic approach in the frame of the 1/N expansion is developed. The method allows us to study various consequences of the conduction electron correlations for the ground state and the low-energy excitations. We analyse the characteristic energy scale in the limit of weak conduction electron interactions. Results are reported for static properties (impurity valence, charge susceptibility, magnetic susceptibility, and specific heat) in the low-temperature limit.Comment: 16 pages, 9 figure

Large-qq expansion of the specific heat for the two-dimensional qq-state Potts model

We have calculated the large-$q$ expansion for the specific heat at the phase transition point in the two-dimensional $q$-state Potts model to the 23rd order in $1/\sqrt{q}$ using the finite lattice method. The obtained series allows us to give highly convergent estimates of the specific heat for $q>4$ on the first order transition point. The result confirm us the correctness of the conjecture by Bhattacharya et al. on the asymptotic behavior of the specific heat for $q \to 4_+$.Comment: 7 pages, LaTeX, 2 postscript figure