They produced no literature, goods, art or bequeathed anything to posterity other than their notoriety as a brutal martial society even that is being questioned. The messy Romans were far better and interesting through their start as a monarchy, transitioning through republic and empire to end as a theological autocracy.
The nearest thing to Spart might be Genghis Khan's Mongols. They Mongols were true nomads whose capital was a tent city. They left no trace of Empire but were secular and bequeathed many important technologies to the world - none of which were their invention. They neither created anything on their own nor built any civilizations but their fame for conquest and administration.
What did the Spartans accomplish?
Edit: Quite a few folks downthread are chiding me for being unaware of the Mongol's contribution to our present society. First, I am comparing them favorably to the Spartans. Second, I have actually been to Ulan Bataar and worked in their cultural institutions preserving Mongol "artefacts" . I have also studied with Mongol teachers and count Mongols as friends. I counsel those counselling me based on books they have read or secondary/tertiary source material on the internet to reconsider their assumptions. Your advice might be well intentioned but off the mark.
The Mongols were tremendous administrators. They were also ruthless nomads who loathed cities, civilization and all its trappings. There is no sign of Genghis' Khan's empire anywhere on this planet. Why? His court was a tent just like his city was a tent city. He also sacked Baghdad and almost every city they came upon including killing the men and raping millions of women and burning their libraries. Yes, they imported postal systems, bureaucracy, paper and whatever else to the world but they also killed 50-100MM people and burned down cities across the middle east for no reason because they did not like them. The descendants of Genghis Khan like Taimur Lame single handedly destroyed vast swaths of Persia, Georgia, Iraq and laid waste to Northern India raising mountains of skulls along the way.
You can keep your postal systems and secular courts, I would like to get some of the cities they sacked and their libraries back.