• Corpus ID: 222177118

Long-range order in discrete spin systems

@article{Peled2020LongrangeOI,
  title={Long-range order in discrete spin systems},
  author={Ron Peled and Yinon Spinka},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
We establish long-range order for discrete nearest-neighbor spin systems on $\mathbb{Z}^d$ satisfying a certain symmetry assumption, when the dimension $d$ is higher than an explicitly described threshold. The results characterize all periodic, maximal-pressure Gibbs states of the system. The results further apply in low dimensions provided that the lattice $\mathbb{Z}^d$ is replaced by $\mathbb{Z}^{d_1}\times\mathbb{T}^{d_2}$ with $d_1\ge 2$ and $d=d_1+d_2$ sufficiently high, where $\mathbb{T… 
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