Critical phenomena and renormalization-group theory

Behaviors of domain walls on the Au-adsorbed $\mathrm{Si}(111)\ensuremath{-}\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ and $6\ifmmode\times\else\texttimes\fi{}6$ surfaces have been investigated by spot-profile-analyzing low-energy electron diffraction and scanning tunneling microscopy. A continuous change from the $\ensuremath{\alpha}\ensuremath{-}\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ pattern to the $\ensuremath{\beta}\ensuremath{-}\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ pattern in diffraction at room temperature has been correlated to the increase in domain-wall density and their characteristic configuration change as a function of Au coverage $\ensuremath{\Theta}=0.76--0.96.$ It has been found that the sharp $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ spikes persists irrespective of the domain-wall morphology. The zigzagging domain walls at $\ensuremath{\Theta}=0.79$ at room temperature are found to transform to roundish ones at 753 K, and finally decompose completely to vanish around 893 K resulting in apparent large domains of $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ structure. Above $\ensuremath{\Theta}=0.96,$ the domain walls are proposed to arrange with a long-range order with $6\ifmmode\times\else\texttimes\fi{}6$ periodicity when the sample is annealed at around 600 K and slowly cooled. On the contrary, metastable amorphous arrangement in the domain walls with average separation of 6a (where a is the substrate lattice period) is formed after annealing followed by quench cooling, which corresponds to the $\ensuremath{\beta}\ensuremath{-}\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ structure.

Structural phase transitions of Si ( 111 ) − ( 3 × 3 ) R 30 ° − Au : Phase transitions in domain-wall configurations

We study by Monte Carlo simulations the influence of bond dilution on the three-dimensional Ising model. This paradigmatic model in its pure version displays a second-order phase transition with a positive specific heat critical exponent $\alpha$
 . According to the Harris criterion disorder should hence lead to a new fixed point characterized by new critical exponents. We have determined the phase diagram of the diluted model, starting from the pure model limit down to the neighbourhood of the percolation threshold. For the estimation of critical exponents, we have first performed a finite-size scaling study, where we concentrated on three different dilutions to check the stability of the disorder fixed point. We emphasize in this work the great influence of the cross-over phenomena between the pure, disorder and percolation fixed points which lead to effective critical exponents dependent on the concentration. In a second set of simulations, the temperature behaviour of physical quantities has been studied in order to characterize the disorder fixed point more accurately. In particular this allowed us to estimate ratios of some critical amplitudes. In accord with previous observations for other models this provides stronger evidence for the existence of the disorder fixed point since the amplitude ratios are more sensitive to the universality class than the critical exponents. Moreover, the question of non-self-averaging at the disorder fixed point is investigated and compared with recent results for the bond-diluted q = 4 Potts model. Overall our numerical results provide evidence that, as expected on theoretical grounds, the critical behaviour of the bond-diluted model is indeed governed by the same universality class as the site-diluted model.

/pdf/bond-dilution-in-the-3d-ising-model-a-monte-carlo-study-40fvsh6nwt.pdf

Bond dilution in the 3D Ising model: a Monte Carlo study

Mechanism and kinetics of color center formation on epitaxial thin films of MgO

We study by Monte Carlo simulations the influence of bond dilution on the three-dimensional Ising model. This paradigmatic model in its pure version displays a second-order phase transition with a positive specific heat critical exponent $\alpha$. According to the Harris criterion disorder should hence lead to a new fixed point characterized by new critical exponents. We have determined the phase diagram of the diluted model, between the pure model limit and the percolation threshold. For the estimation of critical exponents, we have first performed a finite-size scaling study, where we concentrated on three different dilutions. We emphasize in this work the great influence of the cross-over phenomena between the pure, disorder and percolation fixed points which lead to effective critical exponents dependent on the concentration. In a second set of simulations, the temperature behaviour of physical quantities has been studied in order to characterize the disorder fixed point more accurately. In particular this allowed us to estimate ratios of some critical amplitudes. In accord with previous observations for other models this provides stronger evidence for the existence of the disorder fixed point since the amplitude ratios are more sensitive to the universality class than the critical exponents. Moreover, the question of non-self-averaging at the disorder fixed point is investigated and compared with recent results for the bond-diluted $q=4$ Potts model. Overall our numerical results provide evidence that, as expected on theoretical grounds, the critical behaviour of the bond-diluted model is governed by the same universality class as the site-diluted model.

https://arxiv.org/pdf/cond-mat/0402596.pdf

Phase transitions and critical phenomena in strongly chemisorbed adlayers: Influence of defects

Isotope effects at the order-disorder phase transition of the (2 × 2)−2H structure on Ni(111)

The capability of diffraction intensity fluctuations to probe dynamic phenomena at equilibrium is studied. The summation of fluctuations over different domains that scatter incoherently, the role of statistically “white-noise” generated fluctuations and the time necessary to collect a sufficiently long signal are investigated. The factors that determine the number of incoherent regions, and maximize the relative fluctuation without reducing the count rate to such low values that impractically long acquisition times are needed are discussed. Monte Carlo simulations modeling thermally generated step fluctuations are used to illustrate the results.

/pdf/are-equilibrium-fluctuations-detectable-in-diffracted-2egfb6y9wc.pdf

Are equilibrium fluctuations detectable in diffracted intensities

Modifications in desorption kinetics of physisorbed species induced by colour centres on NaCl(100)

Kr and Xe on NaCl(100): pure phases and their miscibility

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