For a d-dimensional 4' lattice field theory consisting of N spins, an asymptotic expansion of expectations about the Ising limit is established in inverse powers of the bare coupling constant A. In the thermodynamic limit (N -+ co), the expansion is expected to be valid in the noncritical region of
A convergent expansion about mean field theory: I. The expansion
β Scribed by James Glimm; Arthur Jaffe; Thomas Spencer
- Publisher
- Elsevier Science
- Year
- 1976
- Tongue
- English
- Weight
- 964 KB
- Volume
- 101
- Category
- Article
- ISSN
- 0003-4916
No coin nor oath required. For personal study only.
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An apparent difference between formulating mean field perturbation theory for @\* field theory via path integrals or via functional differential equations when there are external sources present is shown not to exist when mean lield theory is considered as the N= 1 limit of the O(N) @" field theory.
The optimized expansion for the effective action in quantum field theory is discussed to second order. As an example we use the scalar quantum field theory with \(\lambda \phi^{4}\) interaction in one-dimensional space-time, which is equivalent to quantum mechanics of the anharmonic ascillator. The
The authors thank Dr. R. Dron for his interest in their work on the mechanism of sulphate expansion [I,2]. Indeed, the opinion expressed is different from the "two schools of thought" well-described by Dr. M.D. Cohen [3]. The first school stresses ettringite formation through topochemical reaction a