  As a simple lattice model that exhibits a phase transition, the Ising model
plays a fundamental role in statistical and condensed matter physics. The Ising
transition is realized by physical systems, such as the liquid-vapor
transition. Its continuum limit also furnishes a basic example of interacting
quantum field theories and universality classes. Motivated by a recent hybrid
bootstrap study of the quantum quartic oscillator, we revisit the conformal
bootstrap approach to the 3D Ising model at criticality, without resorting to
positivity constraints. We use at most 10 nonperturbative crossing constraints
at low derivatives from the Taylor expansion around a crossing symmetric point.
The high-lying contributions are approximated by simple analytic formulae
deduced from the lightcone singularity structure. Surprisingly, the low-lying
properties are determined to good accuracy by this computationally very cheap
approach. For instance, the results for the two relevant scaling dimensions
$(\Delta_\sigma,\Delta_\epsilon)\approx (0.518153,1.41278)$ are close to the
most precise rigorous bounds obtained at a much higher computational cost.
