Mitchell Institute for Fundamental Physics & Astronomy
College Station, Texas 77843
Renormalization group methods have been used for almost 50 years to obtain results for critical exponents of conformal field theories (CFTs), while relying on assumptions and approximations that are not rigorously justified. More recently, the numerical conformal bootstrap, a fully nonperturbative method, has proven to be very powerful in calculating critical exponents and other physical observables of unitary CFTs. In this talk we will review the numerical conformal bootstrap method and discuss its applications to 3D CFTs relevant for continuous phase transitions observed in various experiments.