Fluctuation-driven selection at criticality in a frustrated magnetic system: the case of multiple-k partial order on the pyrochlore lattice

Correlated Partial Disorder in a Weakly Frustrated Quantum Antiferromagnet

Partial disorder-the microscopic coexistence of long-range magnetic order and disorder-is a rare phenomenon that has been experimentally and theoretically reported in some Ising- or easy plane-spin systems, driven by entropic effects at finite temperatures. Here, we present an analytical and numerical analysis of the S=1/2 Heisenberg antiferromagnet on the sqrt[3]×sqrt[3]-distorted triangular lattice, which shows that its quantum ground state has partial disorder in the weakly frustrated regime. This state has a 180° Néel ordered honeycomb subsystem coexisting with disordered spins at the hexagon center sites. These central spins are ferromagnetically aligned at short distances, as a consequence of a Casimir-like effect originated by the zero-point quantum fluctuations of the honeycomb lattice.

Intermediate Thermodynamic States Contribute Equally to Free Energy Convergence: A Demonstration with Replica Exchange

We investigate the relationship between the number of intermediate thermodynamic states along a pathway and the precision of free energy estimates. With a sufficient number of states, the asymptotic variance collapses as a function of the total sample size. Our analytical result is corroborated by replica exchange molecular dynamics simulations of model systems in which the neighbor exchange rate exceeds 35%. Precision collapse is also observed in heat capacity estimates based on the multistate Bennett acceptance ratio. In contrast to the relaxation and mean first-passage times, the autocorrelation time of state indices is found to be relevant to free energy convergence.

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.