A new lattice spin model for many self-avoiding polymers is introduced in which the chain length distribution is fully controllable with a single generating ('magnetic') field. The model utilises spins with additional internal symmetry degrees of freedom to impose a causal connectivity of the polymer bonds on the lattice. Use of the method of random fields then produces an equivalent n to 0 limit field theory. The Flory-Huggins theory for a polymer solution emerges simply from this field theory in the mean field approximation. Polymer-polymer interactions between polymer segments on nearest-neighbour lattice are introduced into the field theory, and the low polymer volume fraction limit of the theory reduces to the Edwards type field theory for dilute through semidilute polymer solutions. A sketch is provided towards the treatment of branched polymers with fully controllable chain and branch length distributions and branching probabilities as well as a kinetic polymerisation system governed by specified propagation and termination probabilities.