Abstract

The two-dimensional case occupies a special position in the theory of critical phenomena due to the exact results provided by lattice solutions and, directly in the continuum, by the infinite-dimensional character of the conformal algebra. However, some sectors of the theory, and most notably criticality in systems with quenched disorder and short-range interactions, have appeared out of reach of exact methods and lacked the insight coming from analytical solutions. In this article, we review recent progress achieved implementing conformal invariance within the particle description of field theory. The formalism yields exact unitarity equations whose solutions classify critical points with a given symmetry. It provides new insight in the case of pure systems, as well as the first exact access to criticality in presence of short range quenched disorder. Analytical mechanisms emerge that in the random case allow the superuniversality of some critical exponents and make explicit the softening of first-order transitions by disorder.

Graphic abstract

中文翻译：

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纯系统和无序系统中的粒子，共形不变性和临界性

摘要

由于晶格解的精确结果以及共形代数的无穷维特征，直接在连续体中，二维情况在临界现象理论中占有特殊的位置。但是，该理论的某些领域，尤其是在具有淬灭性无序和短程相互作用的系统中的临界性，似乎超出了精确方法的范围，并且缺乏来自分析解决方案的洞察力。在本文中，我们回顾了在场论的粒子描述内实现共形不变性的最新进展。形式主义产生精确的统一性方程，其解以给定的对称性对临界点进行分类。它为纯系统提供了新的见解，以及在出现短程淬灭性疾病时首次精确进入临界状态。分析机制的出现是在随机情况下允许某些临界指数的超通用性，并明确表明无序化一阶跃迁的软化。

图形摘要