Mean field theory of hole pairs in three dimensions

1991 ◽  
Vol 185-189 ◽  
pp. 1515-1516 ◽  
Author(s):  
Kazuhiko Sakakibara ◽  
Ikuo Ichinose ◽  
Tetsuo Matsui
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Three Dimensions

Computer Simulations and Statistical Theory of Normal Grain Growth in Two and Three Dimensions

2004 ◽  
Vol 467-470 ◽  
pp. 1129-1136 ◽  
Author(s):  
Dana Zöllner ◽  
Peter Streitenberger
Keyword(s):  
Field Theory ◽  
Grain Size ◽  
Size Distribution ◽  
Grain Growth ◽  
Grain Size Distribution ◽  
Mean Field Theory ◽  
Mean Field ◽  
Three Dimensions ◽  
Monte Carlo Algorithm ◽  
Geometric Properties

A modified Monte Carlo algorithm for single-phase normal grain growth is presented, which allows one to simulate the time development of the microstructure of very large grain ensembles in two and three dimensions. The emphasis of the present work lies on the investigation of the interrelation between the local geometric properties of the grain network and the grain size distribution in the quasi-stationary self-similar growth regime. It is found that the topological size correlations between neighbouring grains and the resulting average statistical growth law both in two and three dimensions deviate strongly from the assumptions underlying the classical Lifshitz- Sloyzov-Hillert theory. The average local geometric properties of the simulated grain structures are used in a statistical mean-field theory to calculate the grain size distribution functions analytically. By comparison of the theoretical results with the simulated grain size distributions it is shown how far normal grain growth in two and three dimensions can successfully be described by a mean-field theory and how stochastic fluctuations in the average growth law must be taken into account.

Normal Grain Growth in Three Dimensions: Monte Carlo Potts Model Simulation and Mean-Field Theory

2007 ◽  
Vol 550 ◽  
pp. 589-594 ◽  
Author(s):  
Dana Zöllner ◽  
Peter Streitenberger
Keyword(s):  
Field Theory ◽  
Grain Size ◽  
Monte Carlo ◽  
Distribution Function ◽  
Grain Growth ◽  
Mean Field Theory ◽  
Mean Field ◽  
Size Distribution Function ◽  
Three Dimensions ◽  
Self Similar

A modified Monte Carlo Potts model algorithm for single-phase normal grain growth in three dimensions in presented, which enables an extensive statistical analysis of the growth kinetics and topological properties of the microstructure within the quasi-stationary self-similar coarsening regime. From the mean-field theory an analytical grain size distribution function is derived, which is based on a quadratic approximation of the average self-similar volumetric rate of change as a function of the relative grain size as it has been determined from the simulation. The analytical size distribution function is found to be in excellent agreement with the simulation results.

ALLOY ANALOG APPROACH AND THE GUTZWILLER APPROXIMATION AS PARTICULAR CASES OF A MEAN-FIELD THEORY

1992 ◽  
Vol 06 (20) ◽  
pp. 3341-3352 ◽  
Author(s):  
A.A. ALIGIA ◽  
M. AVIGNON
Keyword(s):  
Field Theory ◽  
Saddle Point ◽  
Mean Field Theory ◽  
Mean Field ◽  
Functional Integral ◽  
Three Dimensions ◽  
Atomic Limit ◽  
Analog Approach ◽  
Metal To Insulator Transition ◽  
Insulating Phase

We develop a new mean field-theory for systems with on-site correlations, like the Hubbard and Anderson models. It consists in a generalization of the saddle-point approximation to the functional integral representation proposed by Kotliar and Ruckenstein to more than one saddle point. It contains also the alloy analog approximation proposed by Hubbard as a particular case. For a half-filled Hubbard model and a model density of states appropriate for three dimensions, we obtain a metal to insulator transition as U increases. The effective Hamiltonian for the insulating phase contains two split bands (rather than only one with an extremely heavy mass) which reproduce correctly the Green’s functions of the atomic limit.

Mean field theory of n-layer unbinding

1993 ◽  
Vol 3 (3) ◽  
pp. 385-393 ◽  
Author(s):  
W. Helfrich
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field
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