Are Multiphase Competition and Order by Disorder the Keys to Understanding Yb(2)Ti(2)O(7)?

If magnetic frustration is most commonly known for undermining long-range order, as famously illustrated by spin liquids, the ability of matter to develop new collective mechanisms in order to fight frustration is perhaps no less fascinating, providing an avenue for the exploration and discovery of unconventional behaviors. Here, we study a realistic minimal model where a number of such mechanisms converge, which, incidentally, pertain to the perplexing quantum spin ice candidate Yb(2)Ti(2)O(7). Specifically, we explain how thermal and quantum fluctuations, optimized by order-by-disorder selection, conspire to expand the stability region of a degenerate continuous U(1) manifold against the classical splayed ferromagnetic ground state that is displayed by the sister compound Yb(2)Ti(2)O(7). The resulting competition gives rise to multiple phase transitions, in striking similitude with recent experiments on Yb(2)Ti(2)O(7) [Lhotel et al., Phys. Rev. B 89, 224419 (2014)]. By combining a gamut of numerical techniques, we obtain compelling evidence that such multiphase competition is a natural engine for the substantial sample-to-sample variability observed in Yb(2)Ti(2)O(7) and is the missing key to ultimately understand the intrinsic properties of this material. As a corollary, our work offers a pertinent illustration of the influence of chemical pressure in rare-earth pyrochlores.