Laser mode and frequency combs, as lasers, are commonly one-dimensional systems. Here we present a construction of multi-dimensional laser-mode lattices (mode hyper-combs) with unique properties. They are obtained from regular 1-dimensional combs by multi-frequency modulation in active mode-locking (AML). The hyper-comb, with near neighbor mode coupling and noise functioning as temperature, is mapped to interacting magnetic-spins lattices in the spherical-model which is one of the few statistical-mechanics systems soluble in all dimensions. The important result is that such systems have, in d>2 dimensions, a phase-transition to a global phase-ordered mode hyper-comb. It can therefore change the nature of AML lasers by capturing very broad coherent frequency bandwidths and obtaining ultimately short and robust pulses. Additionally, the hyper-combs can serve as a rare physical realization of the spherical-model in any dimension.