标题： 非广延统计场论 显示英文标题

标题： Nonextensive statistical field theory

摘要： 我们引入了一种场论方法来描述非广延系统的临界行为，这些系统在其自由度之间表现出全局关联，由非广延参数$q$编码。 作为一些应用，我们报道了，据我们所知，首个关于O($N$)矢量模型的普遍静态和动态$q$-依赖非广延临界指数的解析计算，该计算对所有圈阶和$|q - 1| < 1$均有效。 然后出现了新的非广延O($N$)$_{q}$普适类。 我们采用了六种独立的方法，它们给出了相同的结果。 特别是，非广延二维伊辛系统的数值结果，在所提及的近似下是精确的，它与计算机模拟得到的结果一致，在误差范围内尽可能地接近$q$和$1$。 我们主张此方法可以应用于所有由广延统计场论描述的模型。 结果显示了整体关联性和涨落性之间的相互作用。 显示英文摘要

摘要： We introduce a field-theoretic approach for describing the critical behavior of nonextensive systems, systems displaying global correlations among their degrees of freedom, encoded by the nonextensive parameter $q$. As some applications, we report, to our knowledge, the first analytical computation of both universal static and dynamic $q$-dependent nonextensive critical exponents for O($N$) vector models, valid for all loop orders and $|q - 1| < 1$. Then emerges the new nonextensive O($N$)$_{q}$ universality class. We employ six independent methods which furnish identical results. Particularly, the results for nonextensive 2d Ising systems, exact within the referred approximation, agree with that obtained from computer simulations, within the margin of error, as better as $q$ is closer to $1$. We argue that the present approach can be applied to all models described by extensive statistical field theory as well. The results show an interplay between global correlations and fluctuations.