Document Detail

Dimer packings with gaps and electrostatics.
MedLine Citation:
PMID:  18292229     Owner:  NLM     Status:  In-Data-Review    
Fisher and Stephenson conjectured in 1963 that the correlation function (defined by dimer packings) of two unit holes on the square lattice is rotationally invariant in the limit of large separation between the holes. We consider the same problem on the hexagonal lattice, extend it to an arbitrary finite collection of holes, and present an explicit conjectural answer. In recent work we managed to prove this conjecture in two fairly general cases. The quantity giving the answer can be regarded as the exponential of the negative of the two-dimensional electrostatic energy of a system of charges naturally associated with the holes. We further develop this analogy to electrostatics by presenting two different natural ways to define a field in our setup, and showing that both lead to the electric field, in the limit of large separations between the holes. For one of the fields, this is also stated as a limit shape theorem for random surfaces, with the continuum limit being a sum of helicoids. We conclude by explaining the relationship of our results to previous results in the physics literature on spin correlations in the Ising model.
Mihai Ciucu
Related Documents :
22419389 - Dynamic electrostatic lithography: multiscale on-demand patterning on large-area curved...
22502239 - Acoustic privacy area generation based on simple summation of numerous loudspeaker sign...
17155549 - Double layers and ion phase-space holes in the auroral upward-current region.
22352489 - Response probability distribution of built-up vibro-acoustic systems.
19420459 - High-performance piezoelectric gate diode of a single polar-surface dominated zno nanob...
16386749 - Electrohydrodynamics in hierarchically structured monolithic and particulate fixed beds.
23076579 - Isotope labeling methods for relaxation measurements.
18066219 - Stable 120-mw green output tunable over 2 thz by a second-harmonic generation process i...
15324209 - Anisotropy of acceleration in turbulent flows.
Publication Detail:
Type:  Journal Article; Research Support, U.S. Gov't, Non-P.H.S.     Date:  2008-02-21
Journal Detail:
Title:  Proceedings of the National Academy of Sciences of the United States of America     Volume:  105     ISSN:  1091-6490     ISO Abbreviation:  Proc. Natl. Acad. Sci. U.S.A.     Publication Date:  2008 Feb 
Date Detail:
Created Date:  2008-02-28     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  7505876     Medline TA:  Proc Natl Acad Sci U S A     Country:  United States    
Other Details:
Languages:  eng     Pagination:  2766-72     Citation Subset:  IM    
Department of Mathematics, Indiana University, Bloomington, IN 47405, USA.
Export Citation:
APA/MLA Format     Download EndNote     Download BibTex
MeSH Terms

From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine

Previous Document:  Notch regulates IL-10 production by T helper 1 cells.
Next Document:  Akt and CHIP coregulate tau degradation through coordinated interactions.