论文标题
零温度下的双度模型上的混乱和图灵机
Chaos and Turing Machines on Bidimensional Models at Zero Temperature
论文作者
论文摘要
在均衡统计力学或热力学形式主义中，主要目标之一是描述平衡度量家族的行为，以通过反温度$β$进行参数的潜在参数。在这里，我们将平衡度量视为最大化压力的偏移措施。当系统冻结时，即$β\ rightarrow+\ infty $时，其他结构已经证明了这些度量的混乱行为。 Chazottes和Hochman给出了一个最重要的例子之一，当尺寸较大时，它们证明了在局部恒定潜力的平衡度量的不连贯性。当$β_K\ rightarrow+\ \ iftty $时，对于任何平衡度量的任何序列，都会出现非连贯性。为了描述这样一个例子，我们使用了Aubrun和Sablik所描述的结构，从而改善了用于建造Chazottes和Hochman的Hochman的结果。
In equilibrium statistical mechanics or thermodynamics formalism one of the main objectives is to describe the behavior of families of equilibrium measures for a potential parametrized by the inverse temperature $β$. Here we consider equilibrium measures as the shift invariant measures that maximizes the pressure. Other constructions already prove the chaotic behavior of these measures when the system freezes, that is, when $β\rightarrow+\infty$. One of the most important examples was given by Chazottes and Hochman where they prove the non-convergence of the equilibrium measures for a locally constant potential when the dimension is bigger then 3. In this work we present a construction of a bidimensional example described by a finite alphabet and a locally constant potential in which there exists a subsequence $(β_k)_{k\geq 0}$ where the non-convergence occurs for any sequence of equilibrium measures at inverse of temperature $β_k$ when $β_k\rightarrow+\infty$. In order to describe such an example, we use the construction described by Aubrun and Sablik which improves the result of Hochman used in the construction of Chazottes and Hochman.
