  We consider percolation on $\mathbb{Z}^d$ and on the $d$-dimensional discrete
torus, in dimensions $d \ge 11$ for the nearest-neighbour model and in
dimensions $d>6$ for spread-out models. For $\mathbb{Z}^d$, we employ a wide
range of techniques and previous results to prove that there exist positive
constants $c$ and $C$ such that the slightly subcritical two-point function and
one-arm probabilities satisfy \[ \mathbb{P}_{p_c-\varepsilon}(0 \leftrightarrow
x) \leq \frac{C}{\|x\|^{d-2}} e^{-c\varepsilon^{1/2} \|x\|} \quad \text{ and }
\quad \frac{c}{r^{2}} e^{-C \varepsilon^{1/2}r} \leq
\mathbb{P}_{p_c-\varepsilon}\Bigl(0 \leftrightarrow \partial [-r,r]^d \Bigr)
\leq \frac{C}{r^2} e^{-c \varepsilon^{1/2}r}. \] Using this, we prove that
throughout the critical window the torus two-point function has a "plateau,"
meaning that it decays for small $x$ as $\|x\|^{-(d-2)}$ but for large $x$ is
essentially constant and of order $V^{-2/3}$ where $V$ is the volume of the
torus. The plateau for the two-point function leads immediately to a proof of
the torus triangle condition, which is known to have many implications for the
critical behaviour on the torus, and also leads to a proof that the critical
values on the torus and on $\mathbb{Z}^d$ are separated by a multiple of
$V^{-1/3}$. The torus triangle condition and the size of the separation of
critical points have been proved previously, but our proofs are different and
are direct consequences of the bound on the $\mathbb{Z}^d$ two-point function.
In particular, we use results derived from the lace expansion on
$\mathbb{Z}^d$, but in contrast to previous work on high-dimensional torus
percolation we do not need or use a separate torus lace expansion.
