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We explain how the axioms of Conformal Field Theory are used to makepredictions about critical exponents of continuous phase transitions in threedimensions, via a procedure called the conformal bootstrap. The method assumesconformal invariance of correlation functions, and imposes some relationsbetween correlation functions of different orders. Numerical analysis showsthat these conditions are incompatible unless the critical exponents takeparticular values, or more precisely that they must belong to a small island inthe parameter space.

3D Ising Model: a view from the Conformal Bootstrap Island