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Register a new userTransitions between epitaxial growth regimes: A (1+1)-dimensional kinetic Monte Carlo study
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To study epitaxial thin-film growth, a new model is introduced and extensive kinetic Monte Carlo simulations performed for a wide range of fluxes and temperatures. Varying the deposition conditions, a rich growth diagram is found. The model also reproduces several known regimes and in the limit of low particle mobility a new regime is defined. Finally, a relation is postulated between the temperatures of the kinetic and thermal roughening transitions.
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In this thesis we present a kinetic Monte Carlo model for the description of epitaxial graphene growth. Experimental results suggest a growth mechanism by which clusters of 5 carbon atoms are an intermediate species necessary for nucleation and island growth. This model is proposed by experimentally studying the velocity of growth of islands which is a highly nonlinear function of adatom concentration. In our simulation we incorporate this intermediate species and show that it can explain all other experimental observations: the temperature dependence of the adatom nucleation density, the equilibrium adatom density and the temperature dependence of the equilibrium island density. All these processes are described only by the kinematics of the system.
We perform large-scale Monte Carlo simulations of the classical XY model on a three-dimensional $Ltimes L times L$ cubic lattice using the graphics processing unit (GPU). By the combination of Metropolis single-spin flip, over-relaxation and parallel-tempering methods, we simulate systems up to L=160. Performing the finite-size scaling analysis, we obtain estimates of the critical exponents for the three-dimensional XY universality class: $alpha=-0.01293(48)$ and $ u=0.67098(16)$. Our estimate for the correlation-length exponent $ u$, in contrast to previous theoretical estimates, agrees with the most recent experimental estimate $ u_{rm exp}=0.6709(1)$ at the superfluid transition of $^4$He in a microgravity environment.
We present a worm-type Monte Carlo study of several typical models in the three-dimensional (3D) U(1) universality class, which include the classical 3D XY model in the directed flow representation and its Villain version, as well as the 2D quantum Bose-Hubbard (BH) model with unitary filling in the imaginary-time world-line representation. From the topology of the configurations on a torus, we sample the superfluid stiffness $rho_s$ and the dimensionless wrapping probability $R$. From the finite-size scaling analyses of $rho_s$ and of $R$, we determine the critical points as $T_c ({rm XY}) =2.201, 844 ,1(5)$ and $T_c ({rm Villain})=0.333, 067, 04(7)$ and $(t/U)_c ({rm BH})=0.059 , 729 ,1(8)$, where $T$ is the temperature for the classical models, and $t$ and $U$ are respectively the hopping and on-site interaction strength for the BH model. The precision of our estimates improves significantly over that of the existing results. Moreover, it is observed that at criticality, the derivative of a wrapping probability with respect to $T$ suffers from negligible leading corrections and enables a precise determination of the correlation length critical exponent as $ u=0.671 , 83(18)$. In addition, the critical exponent $eta$ is estimated as $eta=0.038 , 53(48)$ by analyzing a susceptibility-like quantity. We believe that these numerical results would provide a solid reference in the study of classical and quantum phase transitions in the 3D U(1) universality, including the recent development of the conformal bootstrap method.
We investigate by means of Monte Carlo simulations the dynamic phase transition of the two-dimensional kinetic Blume-Capel model under a periodically oscillating magnetic field in the presence of a quenched random crystal-field coupling. We analyze the universality principles of this dynamic transition for various values of the crystal-field coupling at the originally second-order regime of the corresponding equilibrium phase diagram of the model. A detailed finite-size scaling analysis indicates that the observed nonequilibrium phase transition belongs to the universality class of the equilibrium Ising ferromagnet with additional logarithmic corrections in the scaling behavior of the heat capacity. Our results are in agreement with earlier works on kinetic Ising models.
We investigate the critical relaxational dynamics of the S=1/2 Heisenberg ferromagnet on a simple cubic lattice within the Handscomb prescription on which it is a diagrammatic series expansion of the partition function that is computed by means of a Monte Carlo procedure. Using a phenomenological renormalization group analysis of graph quantities related to the spin susceptibility and order parameter, we obtain precise estimates for the critical exponents relations $gamma / u = 1.98pm 0.01 $ and $beta / u = 0.512 pm 0.002$ and for the Curie temperature $k_BT_c/J = 1.6778 pm 0.0002$. The critical correlation time of both energy and susceptibility is also computed. We found that the number of Monte Carlo steps needed to generate uncorrelated diagram configurations scales with the systems volume. We estimate the efficiency of the Handscomb method comparing its ability in dealing with the critical slowing down with that of other quantum and classical Monte Carlo prescriptions.
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