  We study the second-order phase transition in the $d$-dimensional Ising model
with long-range interactions decreasing as a power of the distance $1/r^{d+s}$.
For $s$ below some known value $s_*$, the transition is described by a
conformal field theory without a local stress tensor operator, with critical
exponents varying continuously as functions of $s$. At $s=s_*$, the phase
transition crosses over to the short-range universality class. While the
location $s_*$ of this crossover has been known for 40 years, its physics has
not been fully understood, the main difficulty being that the standard
description of the long-range critical point is strongly coupled at the
crossover. In this paper we propose another field-theoretic description which,
on the contrary, is weakly coupled near the crossover. We use this description
to clarify the nature of the crossover and make predictions about the critical
exponents. That the same long-range critical point can be reached from two
different UV descriptions provides a new example of infrared duality.
