Some properties of adsorbed films of oxygen on tungsten

Roberts, J. K.

doi:10.1098/rspa.1935.0201

Cited by 54 publications

(35 citation statements)

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“…Oxygen atoms form an ordered lattice, belonging to the hexagonal space group P 63/mmc, with the proton configurations in water ice [6,7,10]. Icelike physics also arises in models of frustrated charge order [12,13], proton-bonded (anti-)ferroelectrics [14,15,[21][22][23][24][25], dense polymer melts [26] and dimer models [27,28]. In these systems, violations of the ice rules take on the character of fractionalised charges [13].…”

Section: Introductionmentioning

confidence: 99%

Classical and quantum theories of proton disorder in hexagonal water ice

2016

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It has been known since the pioneering work of Bernal, Fowler and Pauling that common, hexagonal (Ih) water ice is the archetype of a frustrated material : a proton-bonded network in which protons satisfy strong local constraints -the "ice rules" -but do not order. While this proton disorder is well established, there is now a growing body of evidence that quantum effects may also have a role to play in the physics of ice at low temperatures. In this Article we use a combination of numerical and analytic techniques to explore the nature of proton correlations in both classical and quantum models of ice Ih. In the case of classical ice Ih, we find that the ice rules have two, distinct, consequences for scattering experiments -singular "pinch points", reflecting a zero-divergence condition on the uniform polarization of the crystal, and broad, asymmetric features, coming from its staggered polarisation. In the case of the quantum model, we find that the collective quantum tunnelling of groups of protons can convert states obeying the ice rules into a quantum liquid, whose excitations are birefringent, emergent photons. We make explicit predictions for scattering experiments on both classical and quantum ice Ih, and show how the quantum theory can explain the "wings" of incoherent inelastic scattering observed in recent neutron scattering experiments [Bove et al., Phys. Rev. Lett. 103, 165901 (2009)]. These results raise the intriguing possibility that the protons in ice Ih could form a quantum liquid at low temperatures, in which protons are not merely disordered, but continually fluctuate between different configurations obeying the ice rules.

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Section: Introductionmentioning

confidence: 99%

Classical and quantum theories of proton disorder in hexagonal water ice

2016

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“…Monomer-dimer models were introduced in the last century in the physics literature to study the statistical mechanics problem of diatomic oxygen adsorption on tungsten [1] and similar phenomena (see [2] and references therein). Important rigorous results were obtained by Heilmann and Lieb in [3,2], where in particular the absence of phase transition for the pressure as a function of x (and of the monomer density too) was proved for all positive x.…”

Section: Introductionmentioning

confidence: 99%

“…ε(x) turns out to be the expected value of a random variable Y (x) whose distribution is defined as the only fixed point supported in [0,1] of the distributional equation…”

Section: Introductionmentioning

confidence: 99%

Solution of the Monomer–Dimer Model on Locally Tree-Like Graphs. Rigorous Results

Alberici

Contucci

2014

Commun. Math. Phys.

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We consider the monomer-dimer model on sequences of random graphs locally convergent to trees. We prove that the monomer density converges almost surely, in the thermodynamic limit, to an analytic function of the monomer activity. We characterise this limit as the expectation of the solution of a fixed point distributional equation and we give an explicit expression for the limiting pressure per particle.

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“…The problem has a venerable history [1][2][3][4]; it was first introduced in the context of the absorption of molecules on the surface [1]. When a rigid molecule occupies two nearest neighbor (NN) sites on the (square) lattice, it can be regarded as a dimer linking the two NN sites, while an empty site means the presence of a monomer.…”

Section: Introductionmentioning

confidence: 99%

Kosterlitz-Thouless transitions and phase diagrams of the interacting monomer-dimer model on a checkerboard lattice

Li¹,

Li²,

Chen³

2014

Phys. Rev. E

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Using the tensor network approach, we investigate the monomer-dimer models on a checkerboard lattice, in which there are interactions (with strength v) between the parallel dimers on half of the plaquettes. For the fully packed interacting dimer model, we observe a Kosterlitz-Thouless (KT) transition between the low-temperature symmetry breaking and the high-temperature critical phases; for the doped monomer-dimer case with finite chemical potential μ, we also find an order-disorder phase transition which is of second order instead. We use the boundary matrix product state approach to detect the KT and second-order phase transitions and obtain the phase diagrams v-T and μ-T. Moreover, for the noninteracting monomer-dimer model (setting μ=ν=0), we get an extraordinarily accurate determination of the free energy per site (negative of the monomer-dimer constant h_{2}) as f=-0.662798972833746 with the dimer density n=0.638123109228547, both of 15 correct digits.

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Some properties of adsorbed films of oxygen on tungsten

Cited by 54 publications

References 0 publications

Classical and quantum theories of proton disorder in hexagonal water ice

Classical and quantum theories of proton disorder in hexagonal water ice

Solution of the Monomer–Dimer Model on Locally Tree-Like Graphs. Rigorous Results

Kosterlitz-Thouless transitions and phase diagrams of the interacting monomer-dimer model on a checkerboard lattice

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