  For some time now, conformal field theories in two dimensions have been
studied as integrable systems. Much of the success of these studies is related
to the existence of an operator algebra of the theory. In this paper, some of
the extensions of this machinery to the logarithmic case are studied, and used.
More precisely, from Mobius symmetry constraints, the generic three and four
point functions of logarithmic quasiprimary fields are calculated in closed
form for arbitrary Jordan rank. As an example, c=0 disordered systems with
non-degenerate vacua are studied. With the aid of two, three and four point
functions, the operator algebra is obtained and associativity of the algebra
studied.
