We analyze the nature of the phase transition from a smectic stripe phase toa tetragonal phase predicted in analytic studies by Abanov et al. (Phys. Rev. B51, 1023 (1995)) and observed in experiments on ultra-thin magnetic films byVaterlaus et al.(Phys. Rev. Lett. 84, 2247 (2000)). At variance with existentnumerical evidence, for the first time we show results of Monte Carlosimulations on a two-dimensional model with competing exchange and dipolarinteractions showing strong evidence that the transition is a weak first orderone, in agreement with the theoretical predictions of Abanov et al. Besides thenumerical evidence, we give further support to the first order nature of thetransition analyzing a continuum version of the model and showing that itbelongs to a large family of systems, or universality class, in which a firstorder transition driven by fluctuations is expected on quite general grounds.
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