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Starting from an isotropic configuration of intersecting, two-dimensionaltoric codes, we construct a fracton topological phase introduced in Ref. [26],which is characterized by immobile, point- like topological excitations("fractons"), and degenerate ground-states on the torus that are locallyindistinguishable. Our proposal leads to a simple description of the fractonexcitations and of the ground-state as a "loop" condensate, and provides abasis for building new 3D topological orders such as a natural, $Z_{N}$generalization of this fracton phase, which we introduce. We describe the richphase structure of our layered $Z_{N}$ system. By invoking a lattice duality,we demonstrate that when $N \ge 5$, there is an intermediate phase that appearsbetween the decoupled, layered system and the fracton topologically-orderedstate, which opens the possibility of a continuous transition into the fractontopological phase. We conclude by presenting a solvable model, thatinterpolates between the fracton phase and a confined phase in which the phasetransition is first-order.

Isotropic Layer Construction and Phase Diagram for Fracton Topological Phases