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 $\sim 110\mathrm{K}$. The method can be readily applied to study the dielectric properties and phase transitions in other ferroelectric materials at finite temperatures.

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• Permittivity
• Phase transitions by order
• Strain
• Perovskites
• Molecular dynamics