Mathematical Tools
The main mathematical tools to study critical points are renormalization group, which takes advantage of the Russian dolls picture to explain universality and predict numerically the critical exponents, and Variational perturbation theory, which converts divergent perturbation expansions into convergent strong-coupling expansions relevant to critical phenomena. In two-dimensional systems, Conformal field theory is a powerful tool which has discovered many new properties of 2D critical systems, employing the fact that scale invariance, along with a few other requisites, leads to an infinite symmetry group.
Read more about this topic: Critical Phenomena
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