  In this paper we promote the idea of quantum critical lines ({\em inter alia}
surfaces) as opposed to points. A quantum critical line obtains when
criticality at zero temperature is extended over a continuum in a
one-dimensional line. We base our ideas on a simple but exactly solved model
introduced by one of the authors involving a one-dimensional quantum transverse
field Ising model with added 3-spin interaction. While many of the ideas are
quite general, there are other aspects that are not. In particular, a line of
criticality with continuously varying exponents is not captured. However, the
exact solvability of the model gives us considerable confidence in our results.
Although the pure system is analytically exactly solved, the disorder case
requires numerical analyses based on exact computation of the correlation
function in the Pfaffian representation. The disorder case leads to dynamic
structure factor as a function of frequency and wave vector. We expect that the
model is experientally realizable and perhaps many other similar models will be
found to explore quantum critical lines.
