  We identify the strong coupling fishnet diagram with a certain Ising spin
configuration in the lightcone worldsheet description of planar Tr\Phi^3 field
theory. Then, using a mean field formalism, we take the remaining planar
diagrams into account in an average way. The fishnet spin configuration
requires two mean fields \phi,\phi' where the fishnet diagram is the case
\phi=1,\phi'=0. For general values of these fields, the system is then
approximated as a light-cone quantized string with a field dependent effective
string tension T_{eff}(\phi,\phi'). We also calculate the worldsheet energy
density E(\phi,\phi'), and find the field values that minimize it in the
presence of a transverse space infra-red cutoff \epsilon>0. The criterion for
string formation is that the tension in this minimum energy state remains
non-zero as \epsilon goes to 0. In the most simple-minded implementation of the
mean field method, we find that the tension vanishes for weak and moderate
coupling, but for very large coupling stays non-zero. A more elaborate
treatment, taking temporal correlations into account, removes this ``phase
transition'' and the string tension of the minimum energy state vanishes for
all values of the coupling when \epsilon goes to 0. Our mean field analysis
thus suggests that the ``fishnet phase'' of Tr\Phi^3 theory is unstable, and
there is no string formation for any value of the coupling. This is probably a
reasonable outcome given the instability of the underlying theory.
