  It has long been expected that the 3d Ising model can be thought of as a
string theory, where one interprets the domain walls that separate up spins
from down spins as two-dimensional string worldsheets. The usual Ising
Hamiltonian measures the area of these domain walls. This theory has string
coupling of unit magnitude. We add new local terms to the Ising Hamiltonian
that further weight each spin configuration by a factor depending on the genus
of the corresponding domain wall, resulting in a new 3d Ising model that has a
tunable bare string coupling $g_s$. We use a combination of analytical and
numerical methods to analyze the phase structure of this model as $g_s$ is
varied. We study statistical properties of the topology of worldsheets and
discuss the prospects of using this new deformation at weak string coupling to
find a worldsheet description of the 3d Ising transition.
