论文标题
在饱和度方案中POTTS模型的两点函数上
On the two-point function of the Potts model in the saturation regime
论文作者
论文摘要
我们考虑$ \ Mathbb {z}^d $上的随机群集模型与形式的无限范围的相互作用$ j_x =ψ（x）\ Mathsf {e}^{ - ρ（x）} $与$ρ$与$ \ mathbb {z}^d $ and $ $和$ψ$ A subpententer cormection上的$ρ$ a norm a norm我们首先提供最佳标准，以确保存在非平凡的饱和度方案（即$β_ {\ rm sat}（s）（s）（s）> 0 $的存在，使方向上的反相关长度在$ [0，β_{\ rm sat}（s s）$上的$ [0，β_{\ rm rm sat} $），从而在a上进行了定期。然后，在合适的假设下，我们在整个饱和度方案$（0，β_ {\ rm sat}（s））$中得出了两点函数的尖锐渐近（不为Ornstein-cernike形式）。我们还为这类模型获得了许多其他结果，包括相变的清晰度，高于临界温度高于$β$在$β$ $β$的严格单调性（β_{\ rm sat}（s），β_ {\ rm c}）$中。
We consider the Random-Cluster model on $\mathbb{Z}^d$ with interactions of infinite range of the form $J_x = ψ(x)\mathsf{e}^{-ρ(x)}$ with $ρ$ a norm on $\mathbb{Z}^d$ and $ψ$ a subexponential correction. We first provide an optimal criterion ensuring the existence of a nontrivial saturation regime (that is, the existence of $β_{\rm sat}(s)>0$ such that the inverse correlation length in the direction $s$ is constant on $[0,β_{\rm sat}(s))$), thus removing a regularity assumption used in a previous work of ours. Then, under suitable assumptions, we derive sharp asymptotics (which are not of Ornstein-Zernike form) for the two-point function in the whole saturation regime $(0,β_{\rm sat}(s))$. We also obtain a number of additional results for this class of models, including sharpness of the phase transition, mixing above the critical temperature and the strict monotonicity of the inverse correlation length in $β$ in the regime $(β_{\rm sat}(s), β_{\rm c})$.
