  In the Yang-Mills theory, the apparent thickness of the confining string is
known to grow logarithmically when its length increases. The same logarithmic
broadening also happens to strings in other quantum field theories and domain
walls in statistical physics models. Even in quantum field theories, the
correlators used to measure and characterise this phenomenon are analogous to
those in statistical physics. In this paper we describe it using the string
form factor which is a meaningful quantum observable, obtainable in principle
from scattering experiments. We show how the form factor can be obtained from
field correlation functions calculated in lattice Monte Carlo simulations. We
apply this method to 2+1-dimensional scalar theory in the strong coupling
limit, where it is equivalent to the 3D Ising model, and through duality also
to 2+1-dimensional $\mathbb{Z}_2$ gauge theory. We measure the string form
factor by simulating the Ising model, and demonstrate that it displays the same
logarithmic broadening as observed by other quantities.
