The magnetization-energy scaling limit in high dimension

Jo/:el De Coninck; Charles M. Newman

doi:10.1007/BF01334759

The magnetization-energy scaling limit in high dimension

Jo/:el De Coninck, Charles M. Newman

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In the single-phase region (including the critical point) of a nearest-neighbor Ising ferromagnet with zero external field, the block magnetization and energy within the infinite-volume system are, asymptotically for large block size, independent Gaussian variables when the dimension d exceeds four. For other models, including ones with long-range interactions, a sufficient condition for such triviality of the scaling limit is finiteness of the "bubble quantity".

Original language	English (US)
Pages (from-to)	1451-1467
Number of pages	17
Journal	Journal of Statistical Physics
Volume	59
Issue number	5-6
DOIs	https://doi.org/10.1007/BF01334759
State	Published - Jun 1990

Keywords

/gf field theory
Ising model
Scaling limit
block variables
bubble diagram
renormalization group
triviality
upper critical dimension

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/BF01334759

Cite this

@article{8349f8efc80341eaa9a9b0505cfd9482,

title = "The magnetization-energy scaling limit in high dimension",

abstract = "In the single-phase region (including the critical point) of a nearest-neighbor Ising ferromagnet with zero external field, the block magnetization and energy within the infinite-volume system are, asymptotically for large block size, independent Gaussian variables when the dimension d exceeds four. For other models, including ones with long-range interactions, a sufficient condition for such triviality of the scaling limit is finiteness of the {"}bubble quantity{"}.",

keywords = "/gf field theory, Ising model, Scaling limit, block variables, bubble diagram, renormalization group, triviality, upper critical dimension",

author = "{De Coninck}, Jo/:el and Newman, {Charles M.}",

year = "1990",

month = jun,

doi = "10.1007/BF01334759",

language = "English (US)",

volume = "59",

pages = "1451--1467",

journal = "Journal of Statistical Physics",

issn = "0022-4715",

publisher = "Springer New York",

number = "5-6",

}

TY - JOUR

T1 - The magnetization-energy scaling limit in high dimension

AU - De Coninck, Jo/:el

AU - Newman, Charles M.

PY - 1990/6

Y1 - 1990/6

N2 - In the single-phase region (including the critical point) of a nearest-neighbor Ising ferromagnet with zero external field, the block magnetization and energy within the infinite-volume system are, asymptotically for large block size, independent Gaussian variables when the dimension d exceeds four. For other models, including ones with long-range interactions, a sufficient condition for such triviality of the scaling limit is finiteness of the "bubble quantity".

AB - In the single-phase region (including the critical point) of a nearest-neighbor Ising ferromagnet with zero external field, the block magnetization and energy within the infinite-volume system are, asymptotically for large block size, independent Gaussian variables when the dimension d exceeds four. For other models, including ones with long-range interactions, a sufficient condition for such triviality of the scaling limit is finiteness of the "bubble quantity".

KW - /gf field theory

KW - Ising model

KW - Scaling limit

KW - block variables

KW - bubble diagram

KW - renormalization group

KW - triviality

KW - upper critical dimension

UR - http://www.scopus.com/inward/record.url?scp=34249956036&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249956036&partnerID=8YFLogxK

U2 - 10.1007/BF01334759

DO - 10.1007/BF01334759

M3 - Article

AN - SCOPUS:34249956036

SN - 0022-4715

VL - 59

SP - 1451

EP - 1467

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 5-6

ER -

The magnetization-energy scaling limit in high dimension

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this