  We report an experimental confirmation of the power-law relationship between
the critical anisotropy parameter and ion number for the linear-to-zigzag phase
transition in an ionic crystal. Our experiment uses laser cooled calcium ions
confined in a linear radio-frequency trap. Measurements for up to 10 ions are
in good agreement with theoretical and numeric predictions. Implications on an
upper limit to the size of data registers in ion trap quantum computers are
discussed.
