  The entanglement entropy of a quantum critical system can provide new
universal numbers that depend on the geometry of the entangling bipartition. We
calculate a universal number called $\kappa$, which arises when a quantum
critical system is embedded on a two-dimensional torus and bipartitioned into
two cylinders. In the limit when one of the cylinders is a thin slice through
the torus, $\kappa$ parameterizes a divergence that occurs in the entanglement
entropy sub-leading to the area law. Using large-scale Monte Carlo simulations
of an Ising model in 2+1 dimensions, we access the second Renyi entropy, and
determine that, at the Wilson-Fisher (WF) fixed point, $\kappa_{2,\text{WF}} =
0.0174(5)$. This result is significantly different from its value for the
Gaussian fixed point, known to be $\kappa_{2,\text{Gaussian}} \approx
0.0227998$.
