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arXiv 2104.07503math.DS
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有限型子移位与统计力学模型的对应

On the correspondence between Subshifts of Finite Type and Statistical Mechanics Models

Luis Armando Corona, Raul Salgado-Garcia, Edgardo Ugalde

摘要:

R. Burton和J. Steif发展了一种策略来构造允许几个最大熵测度的有限型强不可约子移位的例子。这种策略利用了平衡统计力学和符号动力学之间的对应关系,这种对应关系后来被O。Häggström.在本文中,我们重新审视和讨论这一对应关系的目的是提出一个简化的版本,并暴露一些严格的结果有关的Potts模型和六顶点模型的符号动力学的应用,说明这种对应关系的可能性。

英文摘要:

R. Burton and J. Steif developed a strategy to construct examples of strongly irreducible subshifts of finite type admitting several measures of maximal entropy. This strategy exploits a correspondence between equilibrium statistical mechanics and symbolic dynamics, correspondence which was later formalized by O. Häggström. In this paper, we revisit and discuss this correspondence with the aim of presenting a simplified version of it, and to expose some applications of rigorous results concerning the Potts model and the six-vertex model to symbolic dynamics, illustrating in this way of the possibilities of this correspondence.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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