Trigonal-to-Tetragonal Transition in Stressed SrTi<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>: A Realization of the Three-State Potts Model

Abstract

The trigonal-to-pseudotetragonal structural first-order transition in [111]-stressed SrTi${\mathrm{O}}_{3}$ is shown to be a realization of the continuous three-state Potts model. The measured order-parameter discontinuity at the transition, $〈\ensuremath{\Delta}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\phi}}〉$, depends on the trigonal order parameter $〈{\ensuremath{\phi}}_{[111]}〉\ensuremath{\propto}M$ as $|〈\ensuremath{\Delta}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\phi}}〉|\ensuremath{\propto}{|M|}^{{\ensuremath{\delta}}^{*}}$, with ${\ensuremath{\delta}}^{*}=0.62\ifmmode\pm\else\textpm\fi{}0.10$ (mean-field theory predicts ${\ensuremath{\delta}}^{*}=1$). This agrees with renormalization-group predictions, and proves that the model has a first-order transition even in the fluctuation-dominated region.