论文标题
与贪婪的晶格动物的随机场Potts模型的相关长度下限
Correlation length lower bound for the random-field Potts model with the greedy lattice animal
论文作者
论文摘要
在过去几年中，最近几年的发展是在2020年首次获得的一篇论文中，由于ding和wirth的相关性长度而进行的，我们追求了一个自然的研究方向，这是作者提出的一种自然研究方向，即确认与随机模型的随机模型相关性的相关长度相同，该比例是随机模型的随机模型。为了证明$ \ frac {4} {3} $在相关长度缩放中的出现，随机场potts模型的相关长度缩放与随机场Ising模型的相关长度缩放相吻合，我们指的是由于Talagrand引起的参数，这是由于talagrand引起的，在该范围内，在该模型上，在该模型上，在greedy lattice动物上限制了相应的较低范围的相关范围，相关的范围是相应的相关长度。 $ \ frac {4} {3} $ endents的贡献出现在随机场iSing的相关长度缩放中，随机场potts模型都让人联想到$ \ frac {4} {4} {3} $指示剂在高温下的liouville量子剂量下的上限。
Motivated by recent developments over the past few years in the study of the correlation length of the random-field Ising model due to Ding and Wirth in a paper first available in 2020, we pursue one natural direction of research that the authors propose is of interest, namely in confirming that the same scaling for the correlation length for the random-field Ising model equals that of the random-field Potts model. To demonstrate that the $\frac{4}{3}$ emergence in the correlation length scaling for the random-field Potts model coincides with that correlation length scaling for the random-field Ising model, we refer to arguments due to Talagrand, in which an upper bound on the greedy lattice animal readily provides a corresponding lower bound on the correlation length. Contributions from the $\frac{4}{3}$ exponent appearing in the correlation length scaling for the random-field Ising, and random-field Potts models alike are reminiscent of $\frac{4}{3}$ exponents in upper bounds taken under the Liouville quantum gravity metric in high temperature.
