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EN
The properties of hyperspherical representation where the one-body orbitals are expressed in terms of the square root of the electron density, ρ(r) and the angle functions {θ_{i}(r)}_{i=1,...,N-1}, (R.F. Nalewajski, P.M. Kozlowski, Acta Phys. Pol. A74, 287 (1988)) are discussed, and the expression for the kinetic energy density functional is analyzed. This expression contains the Weizsäcker term plus a correction determined by the angle functions. Taking into account both the limit of only one occupied level and the slowly varying electron density with large N, it is shown that the kinetic energy density functional interpolates correctly between the known results. Finally, an example of a linear harmonic oscillator is given and the relation between the usual orbital pictures is discussed.
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Improved Phase Diagrams of Ashkin-Teller Model

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EN
The phase diagram of the Askhin-Teller model in two dimensions is determined. Numerical calculations are performed for the simple square L × L lattice using transfer matrix technique. Exploiting finite-size scaling all unknown critical lines were obtained with good accuracy. An extended version of the Ashkin-Teller model is also considered within the molecular field renormalization group method and the critical surface for three-parameter odd-parity Hamiltonian is calculated.
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