论文标题
局部吉布斯测量和离域梯度吉布斯的共存在树上
Coexistence of localized Gibbs measures and delocalized gradient Gibbs measures on trees
论文作者
论文摘要
我们研究了用于在整数（或整数晶格）中旋转值的梯度模型，该模型仅取决于位于具有D + 1邻居的常规树上的相邻位点的自旋值的差异。我们首先根据相关转移操作员Q的相关p-norms提供一般条件，该Q确保存在可数的适当吉布斯度量家族。接下来，我们证明在Q的自然条件下，在自然条件下证明了存在离域的梯度Gibbs度量。这意味着，这两种类型的措施共存，包括SOS模型在内的大型模型，以及例如对数增长的潜力产生的重型模型。
We study gradient models for spins taking values in the integers (or an integer lattice), which interact via a general potential depending only on the differences of the spin values at neighboring sites, located on a regular tree with d + 1 neighbors. We first provide general conditions in terms of the relevant p-norms of the associated transfer operator Q which ensure the existence of a countable family of proper Gibbs measures. Next we prove existence of delocalized gradient Gibbs measures, under natural conditions on Q. This implies coexistence of both types of measures for large classes of models including the SOS-model, and heavy-tailed models arising for instance for potentials of logarithmic growth.
