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Publications Influence

Self-avoiding walk in 5 or more dimensions

- D. Brydges, Thomas Spencer
- Mathematics
- 1 March 1985

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

181 27

The random walk representation of classical spin systems and correlation inequalities

- D. Brydges, J. Fröhlich, Thomas Spencer
- Mathematics
- 1 February 1982

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 19- PDF

Mayer expansions and the Hamilton-Jacobi equation

- D. Brydges, T. Kennedy
- Mathematics
- 1 July 1987

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 10

On the construction of quantized gauge fields

- D. Brydges, J. Fröhlich, E. Seiler
- Physics
- 1 September 1981

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 6

Functional integral representations for self-avoiding walk ∗

- D. Brydges, J. Imbrie, G. Slade
- Mathematics, Physics
- 4 June 2009

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

38 6- PDF

Statistical mechanics of the 2-dimensional focusing nonlinear Schrödinger equation

- D. Brydges, G. Slade
- Mathematics
- 1 December 1996

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 5

The mass gap for Higgs models on a unit lattice

- T. Balaban, J. Imbrie, A. Jaffe, D. Brydges
- Physics
- 1 December 1984

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

- D. Brydges, P. Federbush
- Mathematics
- 1 October 1978

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

- D. Brydges, J. Fröhlich, E. Seiler
- Physics
- 1 September 1979

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

- D. Brydges, J. Dimock, T. Hurd
- Mathematics
- 1 November 1998

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