Decimations for Two-dimensional Ising and Rotator Models I
arXiv:2105.07950 · doi:10.1063/5.0057174
Abstract
We extend proofs of non-Gibbsianness of decimated Gibbs measures at low temperatures to include long-range, as well as vector-spin interactions. Our main tools consist in a two-dimensional use of ``Equivalence of boundary conditions'' in the long-range case and an extension of Global specifications for two-dimensional vector spins.
arXiv comment39 pages, 1 figure
References in corpus (21)
- Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations
- First-order transitions for n-vector models in two and more dimensions; rigorous proof
- Provable first-order transitions for liquid crystal and lattice gauge models with continuous symmetries
- 2D models of statistical physics with continuous symmetry: the case of singular interactions
- On Random Field Induced Ordering in the Classical XY Model
- A Finite-Volume Version of Aizenman-Higuchi Theorem for the 2d Ising Model
- Entropic repulsion and lack of the -measure property for Dyson models
- On Phase Transition and Vortex Stability in the Generalized XY Models
- Discrete approximations to vector spin models
- The phase transition in the anisotropic Heisenberg model with long range dipolar interactions
- Renormalization Group in the uniqueness region: weak Gibbsianity and convergence
- Absence of Dobrushin states for long-range Ising models
- Gibbsian representations of continuous specifications: the theorems of Kozlov and Sullivan revisited
- Renormalization group maps for Ising models in lattice gas variables
- Twelve Tales in Mathematical Physics: An Expanded Heinemann Prize Lecture
- Loss and Recovery of Gibbsianness for XY models in external fields
- Pathological Behavior of Renormalization-Group Maps at High Fields and Above the Transition Temperature
- Synchronization and spin-flop transitions for a mean-field XY model in random field
- Absence of renormalization group pathologies in some critical Dyson-Ising ferromagnets
- Introduction to (generalized) Gibbs measures
- Gibbs Measures for Long-Range Ising Models