Abstract
The conformal bootstrap was proposed in the 1970s as a strategy for calculating the properties of second-order phase transitions. After spectacular success elucidating two-dimensional systems, little progress was made on systems in higher dimensions until a recent renaissance beginning in 2008. We report on some of the main results and ideas from this renaissance, focusing on new determinations of critical exponents and correlation functions in the three-dimensional Ising and O(N) models. A renaissance of interest in a numerical technique known as the conformal bootstrap is surveyed, and its implications for the determination of critical exponents in a range of spin models is discussed.
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