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We find the perturbation spectrum of a family of spherically symmetric andcontinuously self-similar (CSS) exact solutions that appear to be relevant forthe critical collapse of scalar field matter in 2+1 spacetime dimensions. Therate of exponential growth of the unstable perturbation yields the criticalexponent. Our results are compared to the numerical simulations of Pretoriusand Choptuik and are inconclusive: We find a CSS solution with exactly oneunstable mode, which suggests that it may be the critical solution, but anotherCSS solution which has three unstable modes fits the numerically found criticalsolution better.Comment: references added, treatment shortene

Perturbations of an exact solution for (2+1)-dimensional critical collapse