D. Brydges

Publications73
h-index24
Citations1,945
Highly Influential Citations126
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Self-avoiding walk in 5 or more dimensions
Using an expansion based on the renormalization group philosophy we prove that for aT step weakly self-avoiding random walk in five or more dimensions the variance of the endpoint is of orderT and… Expand
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The random walk representation of classical spin systems and correlation inequalities
Ferromagnetic lattice spin systems can be expressed as gases of random walks interacting via a soft core repulsion. By using a mixed spinrandom walk representation we present a unified approach to… Expand
  • 277
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Mayer expansions and the Hamilton-Jacobi equation
We review the derivation of Wilson's differential equation in (infinitely) many variables, which describes the infinitesimal change in an effective potential of a statistical mechanical model or… Expand
  • 139
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On the construction of quantized gauge fields
In this paper the construction of the two-dimensional abelian Higgs model begun in two earlier articles is completed. First we show how to remove the remaining ultraviolet cutoff on the gauge field,… Expand
  • 49
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Functional integral representations for self-avoiding walk ∗
We give a survey and unified treatment of functional inte- gral representations for both simple random walk and some self-avoiding walk models, including models with strict self-avoidance, with weak… Expand
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Statistical mechanics of the 2-dimensional focusing nonlinear Schrödinger equation
We study a natural construction of an invariant measure for the 2-dimensional periodic focusing nonlinear Schrödinger equation, with the critical cubic nonlinearity. We find that a phase transition… Expand
  • 31
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The mass gap for Higgs models on a unit lattice
Abstract An isomorphism is established between eertain compact and noncompact formulations of Abelian gauge theory on a lattice. For weak coupling, the mass gap predicted by the Higgs mechanism is… Expand
  • 48
  • 5
A new form of the Mayer expansion in classical statistical mechanics
New expressions are given for the expansion coefficients in the Mayer expansion (and thus the virial expansion). These promise to be useful in applications, as well as provide a simple rigorous proof… Expand
  • 100
  • 5
On the construction of quantized gauge fields. I. General results
In this paper gauge theories are analyzed from the point of view of constructive quantum field theory. Diamagnetic inequalities for general lattice gauge theories are proven. They say that in a local… Expand
  • 101
  • 4
A Non-Gaussian Fixed Point for φ4 in 4−ε Dimensions
Abstract: We consider the φ4 quantum field theory in four dimensions. The Gaussian part of the measure is modified to simulate 4−ε dimensions where ε is small and positive. We give a renormalization… Expand
  • 29
  • 4