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ature [Fig. 20(a)]. And, at T = T$_{N}$ ≈ 0 . 46 < T ∗ , there is a small jump in C$_{v}$ , accompanied by a clear singularity in global order parameter susceptibility χ global T$_{2}$ [Fig. 20(e)]. While there is no true phase transition at T ∗ , it is clear that the bulk of the entropy of the paramagnet is lost in the smooth crossover into the plateau liquid, and not in the first order transition intothe ordered phase. 

So what happens for J$_{3}$ → 0 ? Unfortunately this question is hard to answer by Monte Carlo simulation, as the massive degeneracy of the uuud states translates into many competing local minima in the free energy. However T$_{N}$ is strictly zero for J$_{3}$ = 0 , and there are two obvious scenarios for how this 

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can be achieved. 

The first is that the first–order transition into the ordered phase becomes weaker as T$_{N}$ → 0 , terminating in a critical end point for J$_{3}$ = 0 , T$_{N}$ = 0 . This end point would in fact be multicritical , since many different ordered uuud states can be formed out of the dimer manifold for different choice of long range interactions. Within this scenario, the power–l aw correlations between spins in the plateau liquid for T → 0 could be viewed as evidence of critical fluctuations. The sec - ond scenario is that the first order transition into the order ed phase persists down to T$_{N}$ = 0 . Since an infinite number of 

