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
Famous quotes containing the words mathematical and/or tools:
“It is by a mathematical point only that we are wise, as the sailor or the fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course.”
—Henry David Thoreau (1817–1862)
“At the utmost, the active-minded young man should ask of his teacher only mastery of his tools. The young man himself, the subject of education, is a certain form of energy; the object to be gained is economy of his force; the training is partly the clearing away of obstacles, partly the direct application of effort. Once acquired, the tools and models may be thrown away.”
—Henry Brooks Adams (1838–1918)