scholarly journals Fermion Representations for the 2D and 3D Ising Models

Author(s):  
VI. S. Dotsenko ◽  
A. M. Polyakov
Keyword(s):  
2005 ◽  
Vol 16 (07) ◽  
pp. 1121-1131 ◽  
Author(s):  
J. KAUPUŽS

The surface tension of rough interfaces between coexisting phases in 2D and 3D Ising models are discussed in view of the known results and some original calculations presented in this paper. The results are summarized in a formula, which allows to interpolate the corrections to finite-size scaling between two and three dimensions. The physical meaning of an analytic continuation to noninteger values of the spatial dimensionality d is discussed. Lattices and interfaces with properly defined fractal dimensions should fulfil certain requirements to possibly have properties of an analytic continuation from d-dimensional hypercubes. Here 2 appears as the marginal value of d below which the (d -1)-dimensional interface splits in disconnected pieces. Some phenomenological arguments are proposed to describe such interfaces. They show that the character of the interfacial fluctuations at d< 2 is not the same as provided by a formal analytic continuation from d-dimensional hypercubes with d≥2. It, probably, is true also for the related critical exponents.


2021 ◽  
pp. 127870
Author(s):  
L.Ts. Adzhemyan ◽  
D.A. Evdokimov ◽  
M. Hnatič ◽  
E.V. Ivanova ◽  
M.V. Kompaniets ◽  
...  

2012 ◽  
Vol 26 (14) ◽  
pp. 1250085 ◽  
Author(s):  
TUNCER KAYA

In this paper we present a simple approximate transfer matrix method for 2D and 3D hyper cubic nearest neighbor Ising models with various coordination number z to calculate the corresponding critical coupling strengths Kc. The critical coupling strengths of the Ising ferromagnets are obtained quite accurately by simple improvements over the self-consistent correlated field (SCCF) approximation. The important physical effect included in this work is some of the fluctuation effects of the systems by the help of a reduced transfer matrix method. When used in combination with the accuracy of the average magnetization obtained from the SCCF approximation, this reduced transfer matrix method leads to estimate of Kc more accurate than those obtained from the Bethe–Peierls–Weiss approximation and also SCCF approximation. Therefore, we believe that the approach we refer to as the correlated reduced transfer matrix method is potentially very useful scheme for obtaining approximate values of the critical coupling strengths of the Ising models with a mathematically easy meaner.


Author(s):  
P.M. Rice ◽  
MJ. Kim ◽  
R.W. Carpenter

Extrinsic gettering of Cu on near-surface dislocations in Si has been the topic of recent investigation. It was shown that the Cu precipitated hetergeneously on dislocations as Cu silicide along with voids, and also with a secondary planar precipitate of unknown composition. Here we report the results of investigations of the sense of the strain fields about the large (~100 nm) silicide precipitates, and further analysis of the small (~10-20 nm) planar precipitates.Numerous dark field images were analyzed in accordance with Ashby and Brown's criteria for determining the sense of the strain fields about precipitates. While the situation is complicated by the presence of dislocations and secondary precipitates, micrographs like those shown in Fig. 1(a) and 1(b) tend to show anomalously wide strain fields with the dark side on the side of negative g, indicating the strain fields about the silicide precipitates are vacancy in nature. This is in conflict with information reported on the η'' phase (the Cu silicide phase presumed to precipitate within the bulk) whose interstitial strain field is considered responsible for the interstitial Si atoms which cause the bounding dislocation to expand during star colony growth.


2021 ◽  
Author(s):  
Ruoyang Liu ◽  
Ke Tian Tan ◽  
Yifan Gong ◽  
Yongzhi Chen ◽  
Zhuoer Li ◽  
...  

Covalent organic frameworks offer a molecular platform for integrating organic units into periodically ordered yet extended 2D and 3D polymers to create topologically well-defined polygonal lattices and built-in discrete micropores and/or mesopores.


2012 ◽  
Author(s):  
Michael Sackllah ◽  
Denny Yu ◽  
Charles Woolley ◽  
Steven Kasten ◽  
Thomas J. Armstrong

Author(s):  
Denny Yu ◽  
Michael Sackllah ◽  
Charles Woolley ◽  
Steven Kasten ◽  
Thomas J. Armstrong
Keyword(s):  

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