  The $d$-dimensional long-range Ising model, defined by spin-spin interactions
decaying with the distance as the power $1/r^{d+s}$, admits a second order
phase transition with continuously varying critical exponents. At $s = s_*$,
the phase transition crosses over to the usual short-range universality class.
The standard field-theoretic description of this family of models is strongly
coupled at the crossover. We find a new description, which is instead weakly
coupled near the crossover, and use it to compute critical exponents. The
existence of two complementary UV descriptions of the same long-range fixed
point provides a novel example of infrared duality.
