Uncertainty as a stabilizer of the head-tail ordered phase in carbon-monoxide monolayers on graphite

Abstract

${(\text{CO})}_{1\ensuremath{-}x}{(\text{Ar})}_{x}$ mixtures physisorbed on graphite experimentally display a novel phenomenon of increasing phase-transition temperature (stabilizing the system) with increasing Ar impurity concentration or uncertainty [H. Wiechert and K.-D. Kortmann, Surf. Sci. 441, 65 (1999)]. We develop a two-dimensional Ising-type model that accurately captures the phase transition and its temperature dependence. The anomaly in transition temperature is due to formation of pinwheel regions of CO around Ar atoms. The dilemma of whether the ground state is head-to-head or head-to-tail ordered is reconciled in favor of the latter. The phase-transition curve in the presence of uncertainty in Ar impurity is computed using Monte Carlo (MC) and probabilistic collocation method (PCM). PCM computes the first two moments $\ensuremath{\approx}2000$ times faster than MC.