## Delocalization of uniform graph homomorphisms from \$\mathbb{Z}^2\$ to \$\mathbb{Z}\$. (arXiv:1810.10124v2 [math.PR] UPDATED)

Graph homomorphisms from the \$\mathbb{Z}^d\$ lattice to \$\mathbb{Z}\$ are functions on \$\mathbb{Z}^d\$ whose gradients equal one in absolute value. These functions are the height functions corresponding to proper \$3\$-colorings of \$\mathbb{Z}^d\$ and, in two dimensions, corresponding to the \$6\$-vertex model (square ice). We consider the uniform model, obtained by sampling uniformly such a graph homomorphism subject to boundary conditions. Our main result is that the model delocalizes in two dimensions, having no translation-invariant Gibbs measures. Additional results are obtained in higher dimensions and include the fact that every Gibbs measure which is ergodic under even translations is extremal and that these Gibbs measures are stochastically ordered.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 Graph homomorphisms from the \$\mathbb{Z}^d\$ lattice to \$\mathbb{Z}\$ are functions on \$\mathbb{Z}^d\$ whose gradients equal one in absolute value. These functions are the height functions corresponding to proper \$3\$-colorings of \$\mathbb{Z}^d\$ and, in two dimensions, corresponding to the \$6\$-vertex model (square ice). We consider the uniform model, obtained by sampling uniformly such a graph homomorphism subject to boundary conditions. Our main result is that the model delocalizes in two dimensions, having no translation-invariant Gibbs measures. Additional results are obtained in higher dimensions and include the fact that every Gibbs measure which is ergodic under even translations is extremal and that these Gibbs measures are stochastically ordered.
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