Decimations for two-dimensional Ising and rotator models

@article{DAchille2022DecimationsFT,
  title={Decimations for two-dimensional Ising and rotator models},
  author={Matteo D’Achille and Aernout C. D. van Enter and Arnaud Le Ny},
  journal={Journal of Mathematical Physics},
  year={2022}
}
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. 
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Decimations for One- and Two-dimensional Ising and Rotator Models II: Continuous versus Discrete Symmetries
We show how decimated Gibbs measures which have an unbroken continuous symmetry due to the Mermin-Wagner theorem, although their discrete equivalents have a phase transition, still can become…

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