TY - JOUR
T1 - Voronoi chains, blocks, and clusters in perturbed square lattices
AU - Lazar, Emanuel A.
AU - Shoan, Amir
N1 - Publisher Copyright:
© 2020 IOP Publishing Ltd and SISSA Medialab srl.
PY - 2020/10/22
Y1 - 2020/10/22
N2 - Perturbed lattices provide simple models for studying many physical systems. In this paper we study the distribution of Voronoi chains, blocks, and clusters with prescribed combinatorial features in the perturbed square lattice, generalizing earlier work. In particular, we obtain analytic results for the presence of hexagonally-ordered regions within a square-ordered phase. Connections to high-temperature crystals and to non-equilibrium phase transitions are considered. In an appendix, we briefly consider the site-percolation threshold for this system.
AB - Perturbed lattices provide simple models for studying many physical systems. In this paper we study the distribution of Voronoi chains, blocks, and clusters with prescribed combinatorial features in the perturbed square lattice, generalizing earlier work. In particular, we obtain analytic results for the presence of hexagonally-ordered regions within a square-ordered phase. Connections to high-temperature crystals and to non-equilibrium phase transitions are considered. In an appendix, we briefly consider the site-percolation threshold for this system.
KW - exact results
KW - random geometry
KW - random/ordered microstructure
UR - http://www.scopus.com/inward/record.url?scp=85095590232&partnerID=8YFLogxK
U2 - 10.1088/1742-5468/abb6e3
DO - 10.1088/1742-5468/abb6e3
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AN - SCOPUS:85095590232
SN - 1742-5468
VL - 2020
JO - Journal of Statistical Mechanics: Theory and Experiment
JF - Journal of Statistical Mechanics: Theory and Experiment
IS - 10
M1 - 103204
ER -