On homogenization and scaling limit of some gradient perturbations of a massless free field. (English) Zbl 0871.35010
The authors study the continuum scaling limit of some statistical mechanical models defined by convex Hamiltonians \(H(\varphi)\) which are gradient perturbations of a massless free field. They prove, under suitable assumptions of positivity of the Hessian of the Hamiltonian, a central limit theorem for these models, and show that their long distance behavior is identical to a new homogeneized continuum massless free field. They obtain also new bounds on the 2-point correlation functions of these models.
Reviewer: B.Helffer (Orsay)
MSC:
| 35B27 | Homogenization in context of PDEs; PDEs in media with periodic structure |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 81T25 | Quantum field theory on lattices |
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