  We explain how the axioms of Conformal Field Theory are used to make
predictions about critical exponents of continuous phase transitions in three
dimensions, via a procedure called the conformal bootstrap. The method assumes
conformal invariance of correlation functions, and imposes some relations
between correlation functions of different orders. Numerical analysis shows
that these conditions are incompatible unless the critical exponents take
particular values, or more precisely that they must belong to a small island in
the parameter space.
