MASS GAP, SCALING AND UNIVERSALITY IN THE D = 2 O(3)-SIGMA-MODEL

Using direct mass measurements and different MCRG methods we investigated the onset of asymptotic scaling and the universality of the mass gap. The standard nearest-neighbour action and a modified action with next-to-nearest neighbour coupling were studied up to correlation length ξ ∼ 1090 and ξ ∼ 330, respectively. The different methods give consistently that asymptotic scaling sets in only above ξ ∼ 500 for the standard action, while much earlier, at ξ ∼ 40, for the modified one. In full agreement with universality, the results m = (3.3 ± 0.1)ΛMS and m = (3.4 ± 0.1)ΛMS were obtained for these two cases, respectively. © 1990.