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
Thermodynamic properties of the φ4 lattice field theory near the Ising limit
✍ Scribed by Gunduz Caginalp
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 612 KB
- Volume
- 126
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
For a d-dimensional 4" lattice field theory consisting of N spins with nearest-neighbor interactions, the partition function is transformed for large bare coupling constant A into an Ising-like system with additional neighbor interactions. For d = 2 a mean field approximation is then used to estimate the difference in critical temperature between the lattice 4" field theory and its Ising limit (A = KJ). Expansions are obtained for the susceptibility and specific heat. The critical exponents are shown to be identical to the lsing exponents.
📜 SIMILAR VOLUMES
We show that the mean-field time-dependent equations in the 8 4 theory can be put into a classical noncanonical Hamiltonian framework with a Poisson structure which is a generalization of the standard Poisson bracket. The Heisenberg invariant appears as a structural invariant of the Poisson tensor.
We discuss a simulation of the lattice A~theory in a parallel environment. The computation has been performed in the IBM ECSEC scientific center. The hardware consists of a set often FPS-164 units connected to a host IBM 4381 computer. In system software is the VM/EPEX experimental parallel control