Percolation of the minority spins in high-dimensional Ising models

M. Aizenman; J. Bricmont; J. L. Lebowitz

doi:10.1007/BF01009363

Percolation of the minority spins in high-dimensional Ising models

M. Aizenman, J. Bricmont, J. L. Lebowitz

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17 Scopus citations

Abstract

We present some new results on the region in the β-h plane where the + spins percolate for the nearest neighbor Ising model. In particular, it is shown that in high enough dimensions d there is percolation of the minority spins at inverse temperatures β<β₊ with some β₊>β_c, for which β₊/gb_c≥1/2log(cd), c a constant.

Original language	English (US)
Pages (from-to)	859-865
Number of pages	7
Journal	Journal of Statistical Physics
Volume	49
Issue number	3-4
DOIs	https://doi.org/10.1007/BF01009363
State	Published - Nov 1987
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Correlated percolation
Ising model
Peierls argument
minority spins

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10.1007/BF01009363

Cite this

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title = "Percolation of the minority spins in high-dimensional Ising models",

abstract = "We present some new results on the region in the β-h plane where the + spins percolate for the nearest neighbor Ising model. In particular, it is shown that in high enough dimensions d there is percolation of the minority spins at inverse temperatures β<β+ with some β+>βc, for which β+/gbc≥1/2log(cd), c a constant.",

keywords = "Correlated percolation, Ising model, Peierls argument, minority spins",

author = "M. Aizenman and J. Bricmont and Lebowitz, \{J. L.\}",

year = "1987",

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volume = "49",

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T1 - Percolation of the minority spins in high-dimensional Ising models

AU - Aizenman, M.

AU - Bricmont, J.

AU - Lebowitz, J. L.

PY - 1987/11

Y1 - 1987/11

N2 - We present some new results on the region in the β-h plane where the + spins percolate for the nearest neighbor Ising model. In particular, it is shown that in high enough dimensions d there is percolation of the minority spins at inverse temperatures β<β+ with some β+>βc, for which β+/gbc≥1/2log(cd), c a constant.

AB - We present some new results on the region in the β-h plane where the + spins percolate for the nearest neighbor Ising model. In particular, it is shown that in high enough dimensions d there is percolation of the minority spins at inverse temperatures β<β+ with some β+>βc, for which β+/gbc≥1/2log(cd), c a constant.

KW - Correlated percolation

KW - Ising model

KW - Peierls argument

KW - minority spins

UR - https://www.scopus.com/pages/publications/0001020411

UR - https://www.scopus.com/inward/citedby.url?scp=0001020411&partnerID=8YFLogxK

U2 - 10.1007/BF01009363

DO - 10.1007/BF01009363

M3 - Article

AN - SCOPUS:0001020411

SN - 0022-4715

VL - 49

SP - 859

EP - 865

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 3-4

ER -

Percolation of the minority spins in high-dimensional Ising models

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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