动力系统的广义数论自旋链联系及期望值
Generalized Number Theoretic Spin Chain-Connections to Dynamical Systems and Expectation Values
摘要：
通过引入一个新的参数x>=0，我们推广了数论自旋链，一个基于Farey分数的一维统计模型。这允许我们在链的长度上写递归关系。这些关系与Lewis三项方程密切相关，后者在Selberg函数的研究中非常有用。然后，我们利用这些关系和自旋取向变换。我们发现一个简单的连接与传递算子的模型的动力系统中的不稳定性。此外，我们能够计算某些自旋期望值明确的自由能或相关长度。这些期望值中的一些似乎与相变的机制直接相关。
英文摘要：
We generalize the number theoretic spin chain, a one-dimensional statistical model based on the Farey fractions, by introducing a new parameter x>=0. This allows us to write recursion relations in the length of the chain. These relations are closely related to the Lewis three-term equation, which is useful in the study of the Selberg ζ-function. We then make use of these relations and spin orientation transformations. We find a simple connection with the transfer operator of a model of intermittency in dynamical systems. In addition, we are able to calculate certain spin expectation values explicitly in terms of the free energy or correlation length. Some of these expectation values appear to be directly connected with the mechanism of the phase transition.
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