  Motivated by a possible relativistic string description of hadrons we use a
discretised light-cone quantisation and Lanczos algorithm to investigate the
phase structure of phi^3 matrix field theory in the large N limit. In 1+1
dimensions we confirm the existence of Polyakov's non-critical string theory at
the boundary between parton-like and string-like phases, finding critical
exponents for longitudinal oscillations equal to or consistent with those given
by a mean field argument. The excitation spectrum is finite, possibly discrete.
We calculate light-cone structure functions and find evidence that the
probability Q(x) of a parton in the string carrying longitudinal momentum
fraction between x and x+dx has support on all 0<x<1, despite the average
number of partons being infinite.
