论文标题
离散的高斯模型，I。高温的重量法化基团流动
The Discrete Gaussian model, I. Renormalisation group flow at high temperature
论文作者
论文摘要
离散的高斯模型是晶格高斯游离场，条件是可被估算的。在两个维度上，在足够高的温度下，我们表明它的宏观缩放尺度限制是高斯游离场的倍数。我们的证明始于单个重量法化组步骤，之后，整数价值字段变为平滑场，然后我们使用重级范围化组方法对其进行分析。 本文还为伴侣论文中离散高斯模型的无限梯度梯度状态的缩放限制构建奠定了基础。此外，我们开发了对一般有限范围相互作用的所有估计，并且对范围急剧依赖。我们希望这些估计值为对离散高斯模型在临界温度下的传播版本进行未来分析做准备。
The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integer-valued. In two dimensions, at sufficiently high temperature, we show that its macroscopic scaling limit on the torus is a multiple of the Gaussian free field. Our proof starts from a single renormalisation group step after which the integer-valued field becomes a smooth field which we then analyse using the renormalisation group method. This paper also provides the foundation for the construction of the scaling limit of the infinite-volume gradient Gibbs state of the Discrete Gaussian model in the companion paper. Moreover, we develop all estimates for general finite-range interaction with sharp dependence on the range. We expect these estimates to prepare for a future analysis of the spread-out version of the Discrete Gaussian model at its critical temperature.
