We present a new high-order coupled cluster method (CCM) formalism for the ground states of lattice quantum spin systems for general spin quantum number, s. This new ''general-s'' formalism is found to be highly suitable for a computational implementation, and the technical details of this implementation are given. To illustrate our new formalism we perform high-order CCM calculations for the one-dimensional spin-half and spin-one antiferromagnetic XXZ models and for the one-dimensional spin-half/spin-one ferrimagnetic XXZ model. The results for the ground-state properties of the isotropic points of these systems are seen to be in excellent quantitative agreement with exact results for the special case of the spin-half antiferromagnet and results of density matrix renormalization group (DMRG) calculations for the other systems. Extrapolated CCM results for the sublattice magnetization of the spin-half antiferromagnet closely follow the exact Bethe Ansatz solution, which contains an infinite-order phase transition at D=1. By contrast, extrapolated CCM results for the sublattice magnetization of the spin-one antiferromagnet using this same scheme are seen to go to zero at D % 1.2, which is in excellent agreement with the value for the onset of the Haldane phase for this model. Results for sublattice magnetizations of the ferrimagnet for both the spin-half and spin-one spins are non-zero and finite across a wide range of D, up to and including the Heisenberg point at D=1.

The coupled cluster method (CCM) is applied to a spin-half model at zero temperature which interpolates between a triangular lattice antiferromagnet (TAF) and a Kagomé lattice antiferromagnet (KAF). The strength of the bonds which connect Kagomé lattice sites is J, and the strength of the bonds which link the non-Kagomé lattice sites to the Kagomé lattice sites on an underlying triangular lattice is J ′ . Our results are found to be highly converged, and our best estimate for the ground-state energy per spin for the spin-half KAF (J ′ = 0) of −0.4252 constitutes one of the most accurate results yet found for this model. The amount of classical ordering on the Kagomé lattice sites is also considered, and it is seen that this parameter goes to zero for values of J ′ very close the KAF point. Further evidence is also presented for CCM critical points which reinforce the conjecture that there is a phase near to the KAF point which is much different to that near to the TAF point (J = J ′ ).PACS numbers: 75.10. Jm, 75.50Ee, 03.65.Ca Our knowledge of the zero-temperature properties of lattice quantum spin systems has been enhanced by the existence of exact solutions, mostly for s = 1/2 onedimensional systems, and by approximate calculations for higher quantum spin number and higher spatial dimensionality. Of particular note have been the density matrix renormalisation group (DMRG) calculations [1] for one-dimensional (1D) and quasi-1D spin systems, although the DMRG has, as yet, not been so conclusively applied to systems of higher spatial dimensionality. Similarly, quantum Monte Carlo (QMC) calculations [2,3] at zero temperature are limited by the existence of the infamous sign problem, which in turn is often a consequence of frustration for lattice quantum spin systems. We note that for non-frustrated systems one can often determine a "sign rule" [4,5] which completely circumvents the minus-sign problem.A good example of a spin system for which, as yet, no sign rule has been proven is the spin-half triangular lattice Heisenberg antiferromagnet (TAF). The fixed-node quantum Monte Carlo (FNQMC) method [6] has however been applied to this system with some success, although the results constitute only a variational upper bound for the energy. Other approximate methods [7,8,9,10] have also been successfully applied to the spin-half TAF, and most, but not all, such treatments predict that about 50% of the classical Néel-like ordering on the three equivalent sublattices remains in the quantum case. In particular, series expansion results [7] give a value for the groundstate energy of E g /N =−0.551, although the corresponding value for the amount of remaining classical order of about 20% is almost certainly too low. This spin-half TAF model therefore constitutes a very challenging problem for such approximate methods. However, the spinhalf Kagomé lattice Heisenberg antiferromagnet (KAF) poses an even more difficult problem, because, like the TAF, not only is it highly frustrated and no exactly provable "sign rule" exists...

New global statistical models of nuclidic (atomic) masses based on multilayered feedforward networks are developed. One goal of such studies is to determine how well the existing data, and only the data, determines the mapping from the proton and neutron numbers to the mass of the nuclear ground state. Another is to provide reliable predictive models that can be used to forecast mass values away from the valley of stability. Our study focuses mainly on the former goal and achieves substantial improvement over previous neural-network models of the mass table by using improved schemes for coding and training. The results suggest that with further development this approach may provide a valuable complement to conventional global models.

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