Exact large deviation bounds up to \(T_ c\) for the Ising model in two dimensions
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Publication:1895850
DOI10.1007/BF01192464zbMath0830.60018MaRDI QIDQ1895850
Publication date: 15 January 1996
Published in: Probability Theory and Related Fields (Search for Journal in Brave)
Large deviations (60F10) Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics (82B24) Percolation (82B43) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)
Related Items (26)
Isoperimetry in supercritical bond percolation in dimensions three and higher ⋮ Complete analyticity for 2D Ising completed ⋮ Concentration inequalities for random fields via coupling ⋮ Asymptotic exponential law for the transition time to equilibrium of the metastable kinetic Ising model with vanishing magnetic field ⋮ Fluctuations of shapes of large areas under paths of random walks ⋮ Phase separation for the long range one-dimensional Ising model ⋮ A new look at the interfaces in percolation ⋮ Quasi-polynomial mixing of the 2D stochastic Ising model with ``plus boundary up to criticality ⋮ Critical Ising on the square lattice mixes in polynomial time ⋮ Critical region for droplet formation in the two-dimensional Ising model ⋮ The cellular basis of cell sorting kinetics ⋮ Geometric variational problems of statistical mechanics and of combinatorics ⋮ Shannon-McMillan theorems for discrete random fields along curves and lower bounds for surface-order large deviations ⋮ Surface order large deviations for 2D FK-percolation and Potts models ⋮ On the 2D Ising Wulff crystal near criticality ⋮ Quantitative homogenization of the disordered \(\nabla \phi \) model ⋮ The 2D-Ising model near criticality: a FK-percolation analysis ⋮ Rigorous probabilistic analysis of equilibrium crystal shapes ⋮ Rigorous probabilistic analysis of equilibrium crystal shapes ⋮ Tightness and tails of the maximum in 3D Ising interfaces ⋮ Large deviations in the van der Waals limit ⋮ Surface tension in the dilute Ising model. The Wulff construction ⋮ Random-cluster representation of the Ashkin-Teller model ⋮ Equivalences of the large deviation principle for Gibbs measures and critical balance in the Ising model ⋮ \(N^{3/4}\) law in the cubic lattice ⋮ Constrained variational problem with applications to the Ising model.
Cites Work
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- The Wulff construction and asymptotics of the finite cluster distribution for two-dimensional Bernoulli percolation
- Large deviations for the empirical field of a Gibbs measure
- Random fields
- Large deviations for the 2D Ising model: A lower bound without cluster expansions
- Complete analyticity for 2D Ising completed
- Exponential decay of connectivities in the two-dimensional Ising model
- Discontinuity of the magnetization in one-dimensional \(1/| x-y| ^ 2\) Ising and Potts models.
- Large deviations for Gibbs random fields
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