Search results for "Square lattice"
showing 10 items of 46 documents
Semiflexible macromolecules in quasi-one-dimensional confinement: Discrete versus continuous bond angles
2015
The conformations of semiflexible polymers in two dimensions confined in a strip of width D are studied by computer simulations, investigating two different models for the mechanism by which chain stiffness is realized. One model (studied by molecular dynamics) is a bead-spring model in the continuum, where stiffness is controlled by a bond angle potential allowing for arbitrary bond angles. The other model (studied by Monte Carlo) is a self-avoiding walk chain on the square lattice, where only discrete bond angles (0° and ±90°) are possible, and the bond angle potential then controls the density of kinks along the chain contour. The first model is a crude description of DNA-like biopolymer…
Critical wetting in the square Ising model with a boundary field
1990
The Ising square lattice with nearest-neighbor exchangeJ>0 and a free surface at which a boundary magnetic fieldH1 acts has a second-order wetting transition. We study the surface excess magnetization and the susceptibility ofL×M lattices by Monte Carlo simulation and probe the critical behavior of this wetting transition, applying finite-size scaling methods. For the cases studied, the results are not consistent with the presumably exactly known values of the critical exponents, because the asymptotic critical region has not yet been reached. Implication of our results for critical wetting in three dimensions and for the application of the present model to adsorbed wetting layers at surfac…
Experimental observations of topologically guided water waves within non-hexagonal structures
2020
International audience; We investigate symmetry-protected topological water waves within a strategically engineered square lattice system. Thus far, symmetry protected topological modes in hexagonal systems have primarily been studied in electromagnetism and acoustics, i.e., dispersionless media. Herein, we show experimentally how crucial geometrical properties of square structures allow for topological transport that is ordinarily forbidden within conventional hexagonal structures. We perform numerical simulations that take into account the inherent dispersion within water waves and devise a topological insulator that supports symmetry-protected transport along the domain walls. Our measur…
Indefinitely growing self-avoiding walk.
1985
We introduce a new random walk with the property that it is strictly self-avoiding and grows forever. It belongs to a different universality class from the usual self-avoiding walk. By definition the critical exponent $\ensuremath{\gamma}$ is equal to 1. To calculate the exponent $\ensuremath{\nu}$ of the mean square end-to-end distance we have performed exact enumerations on the square lattice up to 22 steps. This gives the value $\ensuremath{\nu}=0.57\ifmmode\pm\else\textpm\fi{}0.01$.
High-temperature series expansion for the relaxation times of the two dimensional Ising model
1995
We derive the high temperature series expansions for the two relaxation times of the single spin-flip kinetic Ising model on the square lattice. The series for the linear relaxation time τl is obtained with 20 non-trivial terms, and the analysis yields 2.183±0.005 as the value of the critical exponentΔl, which is equal to the dynamical critical exponentz in the two-dimensional case. For the non-linear relaxation time we obtain 15 non-trivial terms, and the analysis leads to the resultsΔnl = 2.08 ± 0.07. The scaling relationΔl −Δnl = β (β being the exponent of the order parameter) seems to be fulfilled, though the error bars ofΔnl are still quite substantial. In addition, we obtain the serie…
Momentum structure of the self-energy and its parametrization for the two-dimensional Hubbard model
2016
We compute the self-energy for the half-filled Hubbard model on a square lattice using lattice quantum Monte Carlo simulations and the dynamical vertex approximation. The self-energy is strongly momentum dependent, but it can be parametrized via the non-interacting energy-momentum dispersion $\varepsilon_{\mathbf{k}}$, except for pseudogap features right at the Fermi edge. That is, it can be written as $\Sigma(\varepsilon_{\mathbf{k}},\omega)$, with two energy-like parameters ($\varepsilon$, $\omega$) instead of three ($k_x$, $k_y$ and $\omega$). The self-energy has two rather broad and weakly dispersing high energy features and a sharp $\omega= \varepsilon_{\mathbf{k}}$ feature at high tem…
Tight-Binding Model for Spontaneous Magnetism of Quantum Dot Lattices
2003
We use a simple tight-binding model to study the magnetism of two-dimensional quantum dot lattices with 1 to 12 electrons per dot. The results show that in the middle of an electron shell the lattice favours antiferromagnetism while with nearly empty or full shells ferromagnetism is favoured. The size of the antiferromagnetic region increases with the coordination number of the dot. A one-dimensional dot lattice shows a spin-Peierls transition. The results for a square lattice are in good agreement with density functional calculations of Koskinen et al.
Application of the Monte Carlo coherent-anomaly method to two-dimensional lattice-gas systems with further-neighbor interactions
1990
A Monte Carlo version of the coherent-anomaly method has been used to determine critical properties of a two-dimensional Ising ferromagnet with nearest- and next-nearest-neighbor interactions and of a series of two-dimensional lattice-gas systems of particles interacting via 6-12 Lennard-Jones potential. It has demonstrated that the method leads to quite accurate determination of critical temperature but is less successful when used to determine the values of critical exponents \ensuremath{\gamma} and \ensuremath{\nu}.
Unmixing of binary alloys by a vacancy mechanism of diffusion: a computer simulation
1991
The initial stages of phase separation are studied for a model binary alloy (AB) with pairwise interactions e AA , e AB , e BB between nearest neighbors, assuming that there is no direct interchange of neighboring atoms possible, but only an indirect one mediated by vacancies (V) occurring in the system at a concentrationc v and which are strictly conserved, as are the concentrationsc A andc B of the two species.A-atoms may jump to vacant sites with jump rateГ A , B-atoms with jump rateГ B (in the absence of interactions). Particular attention is paid to the question to what extent nonuniform distribution of vacancies affects the unmixing kinetics. Our study focuses on the special caseГ A =…
Vibrational excitations in systems with correlated disorder
2007
We investigate a $d$-dimensional model ($d$ = 2,3) for sound waves in a disordered environment, in which the local fluctuations of the elastic modulus are spatially correlated with a certain correlation length. The model is solved analytically by means of a field-theoretical effective-medium theory (self-consistent Born approximation) and numerically on a square lattice. As in the uncorrelated case the theory predicts an enhancement of the density of states over Debye's $\omega^{d-1}$ law (``boson peak'') as a result of disorder. This anomay becomes reinforced for increasing correlation length $\xi$. The theory predicts that $\xi$ times the width of the Brillouin line should be a universal …