论文标题
热力学形式主义和大偏差原理的乘法模型
Thermodynamic formalism and large deviation principle of multiplicative Ising models
论文作者
论文摘要
这项研究的目的是树毛。首先，我们研究了Ising模型的热力学，相对于2-二元双重汉密尔顿人。这扩展了[Chazotte和Redig，Electron的先前结果。 J.可能，2014年]至$ \ Mathbb {n}^d $。其次，我们建立了平均$ \ frac {1} {n} s_n^g $的大偏差原理（LDP），其中$ s_n^g $是由k个k数字为k co-primes的k数字生成的半群。这扩展了先前的结果[Ban等。 indag。数学，2021年]到远程互动的董事会类别。最后，上述结果被推广到多维晶格$ \ mathbb {n}^d，d \ geq1 $。
The aim of this study is tree-fold. First, we investigate the thermodynamics of the Ising models with respect to 2-multiple Hamiltonians. This extends the previous results of [Chazotte and Redig, Electron. J. Probably., 2014] to $\mathbb{N}^d$. Second, we establish the large deviation principle (LDP) of the average $\frac{1}{N} S_N^G$, where $S_N^G$ is a 2-multiple sum along a semigroup generated by k numbers which are k co-primes. This extends the previous results [Ban et al. Indag. Math., 2021] to a board class of the long-range interactions. Finally, the results described above are generalized to the multidimensional lattice $\mathbb{N}^d, d\geq1$.
