Abstract
Measurements of the order-parameter critical exponent $\ensuremath{\beta}$ at the uniaxial-biaxial nematic phase transition in a lyotropic mixture are reported. They reveal a strong dependence of $\ensuremath{\beta}$ on the concentration of the mixture compounds with two distinct intervals of values separated by a discontinuity. This nonuniversal behavior is interpreted as the result of three different contributions, which express the micellar biaxiality and the distribution of the micellar population with respect to biaxiality and volume.
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