Fields on a Random Lattice
Elegant as it is, the proposal by Christ Friedberg and Lee of studying (Euclidean) quantum field theory on a random -as opposed to regular- lattice has not yet attracted a spectacular interest. This is most likely due to the fact that numerical simulations or analytical (for instance strong coupling) expansions seem much more difficult than in the regular lattice case. Spurious localization effects are also involved and not easy to master. These unhappy circumstances should not however hide the merits of a very fascinating subject which comes as close as possible to a cutoff but still translational and rotational invariant field theory fulfilling all reasonable criteria. On the other hand it looks like a first step towards promoting geometry to a dynamical coupled system. Indeed in the realm of lattice models the random one, corresponds to the use of arbitrary coordinate systems, even though the underlying geometry is kept euclidean, this being in principle not necessary.
KeywordsVoronoi Cell Regular Lattice Average Coordination Plane Wave Basis Random Lattice
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- C. Itzykson, in “Non-Perturbative Field Theory and QCD” Proceedings of the Trieste Workshop, R. Lengo, A. Neveu, P. Olesen, G. Parisi editors, World Scientific, Singapore (1983) E.J. Gardner, C. Itzykson, B. Derrida, submitted to J. Phys. AGoogle Scholar
- J.M. Ziman, Models of disorder, Cambridge University Press, 1979Google Scholar
- R. Collins in “Phase Transitions and Critical Phenomena” VoL.2, C. Domb and M.S. Green editors, Academic Press, London (1972)Google Scholar
- R. Zallen in “Fluctuation Phenomena”, E.W. Montroll, J.L. Lebowitz editors, North Holland (1979)Google Scholar
- L.A. Santalo, Integral Geometry and Geometrical probability. Addison-Wesley, Reading, Mass (1976)Google Scholar
- J.M. Drouffe, C. Itzykson “Random Geometry and the Statistics of Two Dimensional Cells” Saclay preprint 1983Google Scholar