论文标题
在某些关键的dyson-asising Ferromagnets中缺乏重新归一化组病理
Absence of renormalization group pathologies in some critical Dyson-Ising ferromagnets
论文作者
论文摘要
Dyson-asision Ferromagnet是具有功率定律相互作用的一维iSing模型。当功率在-1和-2之间时，模型具有相变。 Van Enter和Le ny证明，在足够低的温度下，取消重新归一化组的转换并未定义，因为重新归一化的度量不是Gibbs度量。我们考虑了一个修改模型，其中最近的邻居联轴器比其他耦合大得多。对于包括关键案件的汉密尔顿家族的家庭，我们证明，重新归一化群体转型的第一步可以是为多数统治和分解的严格定义。
The Dyson-Ising ferromagnet is a one-dimensional Ising model with a power law interaction. When the power is between -1 and -2, the model has a phase transition. Van Enter and Le Ny proved that at sufficiently low temperatures the decimation renormalization group transformation is not defined in the sense that the renormalized measure is not a Gibbs measure. We consider a modified model in which the nearest neighbor couplings are much larger than the other couplings. For a family of Hamiltonians which includes critical cases, we prove that the first step of the renormalization group transformation can be rigorously defined for majority rule and decimation.
