论文标题
Gibbs的独特性测量了普通树上$ 4 $ - 州的反铁磁Potts模型
Uniqueness of the Gibbs measure for the $4$-state anti-ferromagnetic Potts model on the regular tree
论文作者
论文摘要
我们表明，Infinite $（d+1）$上的相互作用参数$ W \ in（d+1）$的$ 4 $ - 状态抗铁磁Potts模型，如果$ w \ geq 1- \ geq 1- \ frac {4} {4} {d+1} $ d $ d \ geq geq eq eq 4 $。这很紧张，因为众所周知，当$ 0 \ leq w <1- \ frac {4} {d+1} $和$ d \ geq 4 $时，有多种吉布斯度量。 此外，我们还提供了$（D+1）$ - $ W \ geq 1- \ geq 1- \ frac {3} {3} {d+1} $时的$ 3 $状态potts模型的Gibbs测度的新证明，当$ d \ geq 3 $和$ w \ in（0,1）$ d = 2 $。
We show that the $4$-state anti-ferromagnetic Potts model with interaction parameter $w\in(0,1)$ on the infinite $(d+1)$-regular tree has a unique Gibbs measure if $w\geq 1-\frac{4}{d+1}$ for all $d\geq 4$. This is tight since it is known that there are multiple Gibbs measures when $0\leq w<1-\frac{4}{d+1}$ and $d\geq 4$. We moreover give a new proof of the uniqueness of the Gibbs measure for the $3$-state Potts model on the $(d+1)$-regular tree for $w\geq 1-\frac{3}{d+1}$ when $d\geq 3$ and for $w\in (0,1)$ when $d=2$.
