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The technique of deterministic record and replay aims at faithfully reenacting an earlier program execution. For concurrent programs, it is one of the most important techniques for program understanding and debugging. This demo presents LEAP: an efficient technique as well as a tool prototype to deterministically replay concurrent Java programs on multi-processors without any changes to the host's environment. During execution, LEAP records the thread access orders w.r.t. each shared memory location. The same thread access orders are then enforced in the replay execution to drive the program to the same states. The replay determinism of this approach is underpinned by formal models and a replay theorem developed in this work. Compared to the related approaches, LEAP records much less information, and thus much more efficient.