Temperature-dependent dielectric permittivity and ferroelectricity in strained <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>SrTiO</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:math>

We investigate the dielectric response as a function of temperature and applied strain of the prototypical perovskite ${\mathrm{SrTiO}}_{3}$ using ab initio molecular dynamics to calculate the complex, dynamical, temperature-dependent lattice dielectric function. The results show excellent agreement with experiment. On the application of tensile uniaxial strain, the static susceptibility shows divergence indicative of a ferroelectric transition. We calculate the required critical strain $(3.8%)$ and estimate the critical exponents of the second-order phase transition. We also see the emergence of the antiferrodistortive phase transition at $\ensuremath{\sim}110\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. The method can be readily applied to study the dielectric properties and phase transitions in other ferroelectric materials at finite temperatures.