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A cluster expansion is given for a fermion field moving in an external field according to the interaction ψψϕ in one space dimension.
The Generalised Yukawa Model ( GY 2 ), ± ψφ N +φ 2M , M>N>1, is bounded below, uniformly in a momentum cutoff, and linearly in the volume of a spatial cutoff.
The existence and exponential clustering of correlation functions for a classical coulomb system at low density or high temperature are proven using methods from constructive quantum field theory, the sine gordon transformation and the Glimm, Jaffe, Spencer expansion about mean field theory. This is a vindication of a belief of long standing among physicists, known as Debye screening. That is, because of special properties of the coulomb potential, the configurations of significant probability are those in which the long range parts of r −1 are mostly cancelled, leaving an effective exponentially decaying potential acting between charge clouds. This paper generalizes a previous paper of one of the authors in which these results were obtained for a special lattice system. The present treatment covers the continuous mechanics situation, ...
The strong interaction limit of the discrete-time weakly self-avoiding walk (or Domb--Joyce model) is trivially seen to be the usual strictly self-avoiding walk. For the continuous-time weakly self-avoiding walk, the situation is more delicate, and is clarified in this paper. The strong interaction limit in the continuous-time setting depends on how the fugacity is scaled, and in one extreme leads to the strictly self-avoiding walk, in another to simple random walk. These two extremes are interpolated by a new model of a self-repelling walk that we call the "quick step" model. We study the limit both for walks taking a fixed number of steps, and for the two-point function.
Comment: 14 pages. We have added further references as well as a proof of Corollary 2.2. This version submitted for publication
Comment: 20 pages, 3 figures; v2: Green's function results added
Comment: 14 pages, 2 figures, v2: references, typos
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