Stability of hierarchical interfaces in a random field model. (English) Zbl 0893.60071
Summary: We study a hierarchical model for interfaces in a random-field ferromagnet. We prove that in dimension \(D>3\), at low temperatures and for weak disorder, such interfaces are rigid. Our proof uses renormalization group transformations for stochastic sequences.
MSC:
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 82B24 | Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics |
| 82B28 | Renormalization group methods in equilibrium statistical mechanics |
| 82B44 | Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics |
Keywords:
disordered systems; random-field Ising model; interfaces; hierarchical model; renormalization of stochastic sequencesReferences:
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