  Laser frequency combs, as most lasers, are one-dimensional. Here we present a
realization of d-dimensional laser mode lattices (mode hyper-combs) with unique
properties. They are constructed from regular 1-dimensional combs by
multi-frequency modulation in active mode-locking (AML). The hyper-comb, with
near neighbor mode interaction and noise functioning as temperature, is mapped
to interacting magnetic spin-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 mode-phase-ordered hyper-comb. It changes the nature of AML lasers,
giving ultimately short and robust pulses which can capture very broad
frequency bandwidths. Additionally, the hyper-combs can serve as a rare
physical realization of the spherical-model in any dimension.
