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The phase diagram of the multiple-spin exchange model on the triangularlattice is studied using exact diagonalizations. The two-spin (J_2) andfour-spin (J_4) exchanges have been taken into account for 12, 16, 19, 21, 24,and 27 site samples in the parameter region J_4=0 - 0.25 (for a fixed J_2=1).It is found that the three-sublattice N\'eel ordered state built up by the puretwo-spin exchange can be destroyed by the four-spin exchange, forming aspin-liquid state. The different data suggest that the phase diagram in thisrange of parameters exhibits two phases. The pure J_2 phase is athree-sublattice Neel ordered phase, a small J_4 drives it into a spin-liquidstate with a spin gap filled of a large number of singlets. This spin-liquidphase is not of the same generic kind as the phase studied by Misguich et al.[Phys. Rev. B 60, 1064 (1999)]. It is observed on the finite-size samples thatthe spin liquid phase, as the Neel ordered phase, exhibits a magnetizationplateau at m = 1/3, and for J_4 >0.15 a second plateau atm=1/2. These twoplateaus are associated respectively to the semi-classical orderings uud anduuud.Comment: 6 pages (RevTex), 5 figures (eps). Published versio

From Néel long-range order to spin liquids in the multiple-spin exchange model