RECURSIVE SAMPLING OF PLANAR GRAPHS AND FRACTAL PROPERTIES OF A TWO-DIMENSIONAL QUANTUM GRAVITY

1990 ◽  
Vol 01 (01) ◽  
pp. 165-179 ◽  
Author(s):  
MICHAEL E. AGISHTEIN ◽  
ALEXANDER A. MIGDAL
Keyword(s):  
Monte Carlo ◽  
Random Graphs ◽  
Planar Graphs ◽  
Two Dimensional ◽  
Cubic Graphs ◽  
New Approach ◽  
Standard Methods ◽  
Fractal Properties ◽  
Dimensional Gravity ◽  
Dynamical Triangulation

We describe a new approach to the Monte-Carlo simulations of two-dimensional gravity. Standard dynamical triangulation technique was combined with results of direct enumeration of the cubic graphs. As a result we were able to build large (128K vertices) statistically independent random graphs directly. The quantitative correspondence between our results and those obtained by standard methods has been observed. The algorithm proved to be so efficient that we were able to conduct all the simulations, which usually require the most powerful computers, on an Iris workstation. An opportunity to generate large random graphs allowed us to observe that the internal geometry of random surfaces is more complicated than simple fractals. External geometry also proved to be rather peculiar.

scholarly journals Convergent series for polynomial lattice models with complex actions

2019 ◽  
Vol 34 (30) ◽  
pp. 1950243
Author(s):  
Vasily Sazonov
Keyword(s):  
Monte Carlo ◽  
Lattice Models ◽  
Initial Approximation ◽  
Convergent Series ◽  
Two Dimensional ◽  
Complex Action ◽  
New Approach ◽  
Monte Carlo Techniques ◽  
Sign Problem ◽  
Non Gaussian

Lattice models with complex actions are important for the understanding of matter at finite densities, but not accessible by the standard Monte Carlo techniques due to the sign problem. Here, we propose a new approach aiming to avoid the complex action/sign problem, by extending the method of convergent series (CS) with a non-Gaussian initial approximation. The main properties of the new series are demonstrated on the example of the two-dimensional oscillating integral.

Structures and crystallization of vacuum-deposited amorphous Se and Sb films

1990 ◽  
Vol 48 (4) ◽  
pp. 140-141
Author(s):  
Makoto Shiojiri ◽  
Toshiyuki Isshiki ◽  
Tetsuya Fudaba ◽  
Yoshihiro Hirota
Keyword(s):  
Monte Carlo ◽  
Electron Microscope ◽  
Monte Carlo Method ◽  
Computer Program ◽  
Radial Distribution ◽  
Film Formation ◽  
Amorphous State ◽  
Two Dimensional ◽  
Amorphous Films ◽  
Binding Condition

In hexagonal Se crystal each atom is covalently bound to two others to form an endless spiral chain, and in Sb crystal each atom to three others to form an extended puckered sheet. Such chains and sheets may be regarded as one- and two- dimensional molecules, respectively. In this paper we investigate the structures in amorphous state of these elements and the crystallization.HRTEM and ED images of vacuum-deposited amorphous Se and Sb films were taken with a JEM-200CX electron microscope (Cs=1.2 mm). The structure models of amorphous films were constructed on a computer by Monte Carlo method. Generated atoms were subsequently deposited on a space of 2 nm×2 nm as they fulfiled the binding condition, to form a film 5 nm thick (Fig. 1a-1c). An improvement on a previous computer program has been made as to realize the actual film formation. Radial distribution fuction (RDF) curves, ED intensities and HRTEM images for the constructed structure models were calculated, and compared with the observed ones.

scholarly journals Interface Roughening in Two Dimensions

2021 ◽  
Vol 182 (3) ◽  
Author(s):  
Gernot Münster ◽  
Manuel Cañizares Guerrero
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Capillary Wave ◽  
System Size ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Wave Approximation ◽  
Statistical Field ◽  
Statistical Field Theory ◽  
Interface Roughening

AbstractRoughening of interfaces implies the divergence of the interface width w with the system size L. For two-dimensional systems the divergence of $$w^2$$ w 2 is linear in L. In the framework of a detailed capillary wave approximation and of statistical field theory we derive an expression for the asymptotic behaviour of $$w^2$$ w 2 , which differs from results in the literature. It is confirmed by Monte Carlo simulations.

scholarly journals Two-color two-dimensional terahertz spectroscopy: A new approach for exploring even-order nonlinearities in the nonperturbative regime

2021 ◽  
Vol 154 (15) ◽  
pp. 154203
Author(s):  
Michael Woerner ◽  
Ahmed Ghalgaoui ◽  
Klaus Reimann ◽  
Thomas Elsaesser
Keyword(s):  
Terahertz Spectroscopy ◽  
Two Dimensional ◽  
New Approach ◽  
Even Order

Two-dimensional asynchronous spectrum with auxiliary cross peaks in probing intermolecular interactions

RSC Advances ◽  
2015 ◽  
Vol 5 (107) ◽  
pp. 87739-87749 ◽  
Author(s):  
Xiaopei Li ◽  
Anqi He ◽  
Kun Huang ◽  
Huizhou Liu ◽  
Ying Zhao ◽  
...  
Keyword(s):  
Intermolecular Interaction ◽  
Intermolecular Interactions ◽  
Two Dimensional ◽  
New Approach

A new approach called “asynchronous spectrum with auxiliary peaks (ASAP)” is proposed for generating a 2D asynchronous spectrum to investigate the intermolecular interaction between two solutes (P and Q) dissolved in the same solution.

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