# 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…

## 4 Citations

Rigidity of proper colorings of $\mathbb{Z}^d$

- Mathematics
- 2018

A proper $q$-coloring of a domain in $\mathbb{Z}^d$ is a function assigning one of $q$ colors to each vertex of the domain such that adjacent vertices are colored differently. Sampling a proper…

Finitary codings for gradient models and a new graphical representation for the six‐vertex model

- Computer ScienceRandom Structures & Algorithms
- 2021

The heart of the argument is to devise a suitable tree structure on the clusters of the underlying percolation process (associated to the graphical representation of the given model), which can be revealed piece-by-piece via exploration and deduce a volume-order large deviation estimate for the energy.

Uniqueness for the q-state antiferromagnetic Potts model on the regular tree

- MathematicsArXiv
- 2021

An elementary proof for the uniqueness regime of general q-state antiferromagnetic Potts model on the d-ary tree is presented and the exact exponential decay rate in all of the subcritical regime, and power law decay rate at the critical temperature is obtained.

From hard spheres to hard-core spins

- Physics
- 2021

A system of hard spheres exhibits physics that is controlled only by their density. This comes about because the interaction energy is either infinite or zero, so all allowed configurations have…

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