  We study the spectrum of two dimensional coupled arrays of continuum
one-dimensional systems by wedding a density matrix renormalization group
procedure to a renormalization group improved truncated spectrum approach. To
illustrate the approach we study the spectrum of large arrays of coupled
quantum Ising chains. We demonstrate explicitly that the method can treat the
various regimes of chains, in particular the three dimensional Ising ordering
transition the chains undergo as a function of interchain coupling.
