We present a realization and first experimental results of a conceptual d-dimensional laser mode lattices (mode hyper-combs). 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. Such systems have in d>2 dimensions, a phase-transition to a global mode-phase-ordered hyper-comb. Such lasers can have unique properties for generating short pulses compared to regular AML, by capturing very broad frequency bandwidths. Additionally, the hyper-combs can serve as a rare physical realization of the spherical-model in any dimension. We report on preliminary experimental results on the pulsation transition in "three-dimensional" AML.