The danger of iteration methods
- 1 January 1983
- journal article
- Published by EDP Sciences in Journal de Physique Lettres
- Vol. 44 (22) , 889-895
- https://doi.org/10.1051/jphyslet:019830044022088900
Abstract
When a Hamiltonian K depends on variables ϕi, the values of these variables which minimize K satisfy the equations ∂K/∂ϕ i = 0. If this set of equations is solved by iteration, there is no guarantee that the solution is the one which minimizes K. In the case of a harmonic system with a random potential periodic with respect to the ϕ i's, the fluctuations have been calculated by Efetov and Larkin by means of the iteration method. The result is wrong in the case of a strong disorder. Even in the weak disorder case, it is wrong for a one-dimensional system and for a finite system of 2 particles. It is argued that the results obtained by iteration are always wrong, and that between 2 and 4 dimensions, spin-pair correlation functions decay like powers of the distance, as found by Aharony and Pytte for another modelKeywords
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