Coarsening in 2D slabs

Michael Damron; Hana Kogan; Charles M. Newman; Vladas Sidoravicius

doi:10.1007/978-1-4939-0339-9_2

Coarsening in 2D slabs

Michael Damron, Hana Kogan, Charles M. Newman, Vladas Sidoravicius

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We study coarsening; that is, the zero-temperature limit of Glauber dynamics in the standard Ising model on slabs S_k = Z² × {0,…, k − 1} of all thicknesses k ≥ 2 (with free and periodic boundary conditions in the third coordinate).We show that with free boundary conditions, for k ≥ 3, some sites fixate for large times and some do not, whereas for k = 2, all sites fixate.With periodic boundary conditions, for k ≥ 4, some sites fixate and others do not, while for k = 2 and 3, all sites fixate.

Original language	English (US)
Title of host publication	Topics in Percolative and Disordered Systems
Editors	Gérard Ben Arous, Pablo A. Ferrari, Alejandro F. Ramírez, Vladas Sidoravicius, Maria Eulália Vares, Charles M. Newman
Publisher	Springer New York LLC
Pages	15-22
Number of pages	8
ISBN (Electronic)	9781493903382
DOIs	https://doi.org/10.1007/978-1-4939-0339-9_2
State	Published - 2014
Event	Pan American Advanced Studies Institute, PASI 2012 - Santiago, Chile Duration: Jan 3 2012 → Jan 14 2012

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	69
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Other

Other	Pan American Advanced Studies Institute, PASI 2012
Country/Territory	Chile
City	Santiago
Period	1/3/12 → 1/14/12

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/978-1-4939-0339-9_2

Cite this

Damron, M., Kogan, H., Newman, C. M., & Sidoravicius, V. (2014). Coarsening in 2D slabs. In G. B. Arous, P. A. Ferrari, A. F. Ramírez, V. Sidoravicius, M. E. Vares, & C. M. Newman (Eds.), Topics in Percolative and Disordered Systems (pp. 15-22). (Springer Proceedings in Mathematics and Statistics; Vol. 69). Springer New York LLC. https://doi.org/10.1007/978-1-4939-0339-9_2

Coarsening in 2D slabs. / Damron, Michael; Kogan, Hana; Newman, Charles M. et al.
Topics in Percolative and Disordered Systems. ed. / Gérard Ben Arous; Pablo A. Ferrari; Alejandro F. Ramírez; Vladas Sidoravicius; Maria Eulália Vares; Charles M. Newman. Springer New York LLC, 2014. p. 15-22 (Springer Proceedings in Mathematics and Statistics; Vol. 69).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Damron, M, Kogan, H, Newman, CM & Sidoravicius, V 2014, Coarsening in 2D slabs. in GB Arous, PA Ferrari, AF Ramírez, V Sidoravicius, ME Vares & CM Newman (eds), Topics in Percolative and Disordered Systems. Springer Proceedings in Mathematics and Statistics, vol. 69, Springer New York LLC, pp. 15-22, Pan American Advanced Studies Institute, PASI 2012, Santiago, Chile, 1/3/12. https://doi.org/10.1007/978-1-4939-0339-9_2

@inproceedings{dff75faba396474ea15338f79da4a772,

title = "Coarsening in 2D slabs",

abstract = "We study coarsening; that is, the zero-temperature limit of Glauber dynamics in the standard Ising model on slabs Sk = Z2 × {0,…, k − 1} of all thicknesses k ≥ 2 (with free and periodic boundary conditions in the third coordinate).We show that with free boundary conditions, for k ≥ 3, some sites fixate for large times and some do not, whereas for k = 2, all sites fixate.With periodic boundary conditions, for k ≥ 4, some sites fixate and others do not, while for k = 2 and 3, all sites fixate.",

author = "Michael Damron and Hana Kogan and Newman, {Charles M.} and Vladas Sidoravicius",

note = "Funding Information: The research of H. K. is supported by NSF grant OISE-0730136. Funding Information: The research of V. S. is supported by CNPq grants PQ 308787/2011-0 and 484801/2011-2. Funding Information: The research of M. D. is supported by NSF grants DMS-0901534 and DMS-1007626. Funding Information: The research of C. M. N. is supported by NSF grants OISE-0730136, DMS-1007524 and DMS-1007626. Publisher Copyright: {\textcopyright} Springer Science+Business Media NewYork 2014.; Pan American Advanced Studies Institute, PASI 2012 ; Conference date: 03-01-2012 Through 14-01-2012",

year = "2014",

doi = "10.1007/978-1-4939-0339-9_2",

language = "English (US)",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "15--22",

editor = "Arous, {G{\'e}rard Ben} and Ferrari, {Pablo A.} and Ram{\'i}rez, {Alejandro F.} and Vladas Sidoravicius and Vares, {Maria Eul{\'a}lia} and Newman, {Charles M.}",

booktitle = "Topics in Percolative and Disordered Systems",

}

TY - GEN

T1 - Coarsening in 2D slabs

AU - Damron, Michael

AU - Kogan, Hana

AU - Newman, Charles M.

AU - Sidoravicius, Vladas

N1 - Funding Information: The research of H. K. is supported by NSF grant OISE-0730136. Funding Information: The research of V. S. is supported by CNPq grants PQ 308787/2011-0 and 484801/2011-2. Funding Information: The research of M. D. is supported by NSF grants DMS-0901534 and DMS-1007626. Funding Information: The research of C. M. N. is supported by NSF grants OISE-0730136, DMS-1007524 and DMS-1007626. Publisher Copyright: © Springer Science+Business Media NewYork 2014.

PY - 2014

Y1 - 2014

N2 - We study coarsening; that is, the zero-temperature limit of Glauber dynamics in the standard Ising model on slabs Sk = Z2 × {0,…, k − 1} of all thicknesses k ≥ 2 (with free and periodic boundary conditions in the third coordinate).We show that with free boundary conditions, for k ≥ 3, some sites fixate for large times and some do not, whereas for k = 2, all sites fixate.With periodic boundary conditions, for k ≥ 4, some sites fixate and others do not, while for k = 2 and 3, all sites fixate.

AB - We study coarsening; that is, the zero-temperature limit of Glauber dynamics in the standard Ising model on slabs Sk = Z2 × {0,…, k − 1} of all thicknesses k ≥ 2 (with free and periodic boundary conditions in the third coordinate).We show that with free boundary conditions, for k ≥ 3, some sites fixate for large times and some do not, whereas for k = 2, all sites fixate.With periodic boundary conditions, for k ≥ 4, some sites fixate and others do not, while for k = 2 and 3, all sites fixate.

UR - http://www.scopus.com/inward/record.url?scp=84959320649&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959320649&partnerID=8YFLogxK

U2 - 10.1007/978-1-4939-0339-9_2

DO - 10.1007/978-1-4939-0339-9_2

M3 - Conference contribution

AN - SCOPUS:84959320649

T3 - Springer Proceedings in Mathematics and Statistics

SP - 15

EP - 22

BT - Topics in Percolative and Disordered Systems

A2 - Arous, Gérard Ben

A2 - Ferrari, Pablo A.

A2 - Ramírez, Alejandro F.

A2 - Sidoravicius, Vladas

A2 - Vares, Maria Eulália

A2 - Newman, Charles M.

PB - Springer New York LLC

T2 - Pan American Advanced Studies Institute, PASI 2012

Y2 - 3 January 2012 through 14 January 2012

ER -

Coarsening in 2D slabs

Abstract

Publication series

Other

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this