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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 tofight 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 Yb2Ti20 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 Yb2Sn20 7. The resulting competition gives rise to multiple phase transitions, in striking similitude with recent experiments on Yb2Ti20 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 Yb2Ti20 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 pyrochlor [ABSTRACT FROM AUTHOR]

Accidental ground state degeneracies-those not a consequence of global symmetries of the Hamiltonian-are inevitably lifted by fluctuations, often leading to long-range order, a phenomenon known as "order-by-disorder" (ObD). The detection and characterization of ObD in real materials currently lacks clear, qualitative signatures that distinguish ObD from conventional energetic selection. We show that for order by thermal disorder (ObTD) such a signature exists: a characteristic temperature dependence of the fluctuation-induced pseudo-Goldstone gap. We demonstrate this in a minimal two-dimensional model that exhibits ObTD, the ferromagnetic Heisenberg-compass model on a square lattice. Using spin-dynamics simulations and self-consistent mean-field calculations, we determine the pseudo-Goldstone gap, Δ, and show that at low temperatures it scales as the square root of temperature, sqrt[T]. We establish that a power-law temperature dependence of the gap is a general consequence of ObTD, showing that all key features of this physics can be captured in a simple model of a particle moving in an effective potential generated by the fluctuation-induced free energy.

The EtMe(3)P and EtMe(3)Sb triangular organic salts are distinguished from other Pd[(dmit)(2)] based salts, as they display valence bond and no long-range order, respectively. Under pressure, a superconducting phase is revealed in EtMe(3)P near the boundary of valence bond order. We use slave-rotor theory with an enlarged unit cell to study competition between uniform and broken translational symmetry states, offering a theoretical framework capturing the superconducting, valence bond order, spin liquid, and metallic phases on an isotropic triangular lattice. Our finite temperature phase diagram manifests a remarkable resemblance to the phase diagram of the EtMe(3)P salt, where the reentrant transition of insulator-metal-insulator type can be explained by an entropy difference between the metal and U(1) spin liquid. We predict different temperature dependence of the specific heat between the spin liquid and metal.