Phase transition in the lattice gross-neveu model

The confining properties of the leading logarithm approximation to the effective lagrangian $\text{L}\text{= F}{}^2\text{/2g}{}^2\text{(t)}$ [ with g(t) a running coupling function of t = log(F²/μ⁴)] are seen to disappear when the second and the third approximations of the β-function power series expansion are considered.     

A procedure to obtain an accurate approximation to a full CI wavefunction

Based on Jacobi elementary rotations, a simple, elegant procedure to obtain approximate CI wavefunctions is discussed. Essentially, a sequence of (2 x 2) matrices is builtup, and the eigenvector attached to the lowest eigenvalue is used to construct a stepwise set of coefficients, which become a very good approximation to theexact Cl result. Full CI calculations could easily be reached in this way. An example formed by some atoms of the He isoelectronic sequence is provided in order to test the flexibility and accuracy of the procedure. A Fortran 90 code is available.     

Another way to implement the Powell formula for updating Hessian matrices related to transition structures

A way to update the Hessian matrix according to the Powell formula is given. With this formula one does not need to store the full Hessian matrix at any iteration. A method to find transition structures, which is a combination of the quasiNewton–Raphson augmented Hessian algorithm with the proposed Powell update scheme, is also given. The diagonalization of the augmented Hessian matrix is carried out by Lanczoslike methods. In this way, during all the optimization process, one avoids to store full matrices.     

Remarks on large-scale matrix diagonalization using a Lagrange–Newton–Raphson minimization in a subspace

We present a matrix diagonalization method where the diagonalization is carried out through a normal Lagrange–Newton–Raphson method solved in a subspace. The subspace is generated using the correction vector that predicts the standard Lagrange–Newton–Raphson formula in the full space. Some numerical examples and the performance of the algorithm are given. Received: 16 February 1999 / Accepted: 10 May 1999 / Published online: 9 September 1999     

EMP as a similarity measure: a geometric point of view

Soft Coulomb potentials constructed by multiplying the classical potential by a Gaussian function (or a linear combination of them) permit to consider a wide family of distributions which limit with the classical potential when the exponent becomes infinite. Soft Coulomb potentials can be employed as potential operators with first order density functions in order to compute families of soft electrostatic molecular potentials (EMP) for any quantum object. The soft EMP family possesses two interesting computational features: being not only formally equivalent to classical EMP, but finite everywhere, even at the atomic nuclei. The structure of the soft Coulomb operator family yielding soft EMP can be easily related with a quantum similarity integral feature.     

Rayleigh–Schrödinger perturbation theory: Practical implementation of matrix and vector formalisms and description of an heuristic sufficiency convergence criterion

Starting from previous work, where Rayleigh–Schrödinger perturbation theory has been reformulated in matrix form, a practical algorithm implementation is described using both full matrix and vector alternatives. An heuristic convergence sufficiency criterion based on Gershgorin discs is also presented. Some numerical examples related to atomic CI computations are reported to illustrate the theoretical framework.