Chaotic dependence on temperature refers to the phenomenon of divergence of Gibbs measures as the temperature approaches a certain value. Models with chaotic behaviour near zero temperature have multiple ground states, none of which are stable. We study the class of uniformly chaotic models, that is, those in which, as the temperature goes to zero, every choice of Gibbs measures accumulates on the entire set of ground states. We characterise the possible sets of ground states of uniformly chaotic finite-range models up to computable homeomorphisms. Namely, we show that the set of ground states of every model with finite-range and rational-valued interactions is topologically closed and connected, and belongs to the class $\Pi_2$ of the arithmetical hierarchy. Conversely, every $\Pi_2$-computable, topologically closed and connected set of probability measures can be encoded (via a computable homeomorphism) as the set of ground states of a uniformly chaotic two-dimensional model with finite-range rational-valued interactions.
翻译：在温度接近零温度的混乱行为模型中,没有一种是稳定的。我们研究的是统一混乱模式的类别,即当温度降到零时,每选择一种Gibbs测量方法都会积累在整个一组地面状态。我们用可比较的原貌形态来描述单一混乱的有限范围模型中可能存在的一组地面状态。也就是说,我们显示,每个具有有限和合理估值相互作用的模型的地面状态都是从结构上封闭和连接的,属于计算等级的$\Pi_2美元。反之,每一组可计算、可计算、可统计封闭和相互关联的概率计量方法都可以(通过可比较的原貌形态学)被编码成一套具有有限和合理估值相互作用的单一混乱两维模型的地面状态。
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