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Perovskites like LaAlO3 (or SrTiO3) undergo displacive structural phasetransitions from a cubic crystal to a trigonal (or tetragonal) structure. Formany years, the critical exponents in both these types of transitions have beenfitted to those of the isotropic three-components Heisenberg model. However,field theoretical calculations showed that the isotropic fixed point of therenormalization group is unstable, and renormalization group iterations floweither to a cubic fixed point or to a fluctuation-driven first-ordertransition. Here we show that these two scenarios correspond to the cubic totrigonal and to the cubic to tetragonal transitions, respectively. In bothcases, the critical behavior is described by slowly varying effective criticalexponents, which exhibit universal features. For the trigonal case, we predicta crossover of the effective exponents from their Ising values to their cubicvalues (which are close to the isotropic ones). For the tetragonal case, theeffective exponents can have the isotropic values over a wide temperaturerange, before exhibiting large changes en route to the first-order transition.New renormalization group calculations near the isotropic fixed point in threedimensions are presented and used to estimate the effective exponents, anddedicated experiments to test these predictions are proposed. Similarpredictions apply to cubic magnetic and ferroelectric systems.

Different critical behaviors in cubic to trigonal and tetragonal perovskites