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Two-dimensional phase transition models and λφ4 field theory. / Sokolov, A. I.

в: Journal of Physical Studies, Том 10, № 4, 2006, стр. 351-357.

Результаты исследований: Научные публикации в периодических изданиях › Обзорная статья › Рецензирование

Harvard

Sokolov, AI 2006, 'Two-dimensional phase transition models and λφ4 field theory', Journal of Physical Studies, Том. 10, № 4, стр. 351-357.

APA

Sokolov, A. I. (2006). Two-dimensional phase transition models and λφ4 field theory. Journal of Physical Studies, 10(4), 351-357.

Vancouver

Sokolov AI. Two-dimensional phase transition models and λφ4 field theory. Journal of Physical Studies. 2006;10(4):351-357.

Author

Sokolov, A. I. / Two-dimensional phase transition models and λφ4 field theory. в: Journal of Physical Studies. 2006 ; Том 10, № 4. стр. 351-357.

BibTeX

@article{89aa14d870f94ad599a6506b887114b2,
title = "Two-dimensional phase transition models and λφ4 field theory",
abstract = "An overview is given of the results obtained recently in the course of renormalization-group (RG) study of two-dimensional (2D) models. RG functions of the two-dimensional n-vector λφ4 Euclidean field theory are written down up to the five-loop terms and perturbative series are resummed by the Pad{\'e} - Borel - Leroy techniques. An account for the five-loop term is shown to shift the Wilson fixed point only briefly, leaving it outside the segment formed by the results of the lattice calculations. This is argued to reflect the influence of the non-analytical contribution to the β-function. The evaluation of the critical exponents for n = 1, n = 0 and n = - 1 in the five-loop approximation and comparison of the results with known exact values confirm the conclusion that non-analytical contributions are visible in two dimensions. The estimates obtained on the base of pseudo-ε{lunate} expansions originating from the 5-loop 2D RG series are also discussed.",
keywords = "Critical exponents, Five-loop expansions, Ising and n-vector models, Pseudo-ε expansion, Renormalization group, Sextic effective coupling",
author = "Sokolov, {A. I.}",
year = "2006",
language = "English",
volume = "10",
pages = "351--357",
journal = "Journal of Physical Studies",
issn = "1027-4642",
publisher = "Ivan Franko National University of Lviv",
number = "4",

}

RIS

TY - JOUR

T1 - Two-dimensional phase transition models and λφ4 field theory

AU - Sokolov, A. I.

PY - 2006

Y1 - 2006

N2 - An overview is given of the results obtained recently in the course of renormalization-group (RG) study of two-dimensional (2D) models. RG functions of the two-dimensional n-vector λφ4 Euclidean field theory are written down up to the five-loop terms and perturbative series are resummed by the Padé - Borel - Leroy techniques. An account for the five-loop term is shown to shift the Wilson fixed point only briefly, leaving it outside the segment formed by the results of the lattice calculations. This is argued to reflect the influence of the non-analytical contribution to the β-function. The evaluation of the critical exponents for n = 1, n = 0 and n = - 1 in the five-loop approximation and comparison of the results with known exact values confirm the conclusion that non-analytical contributions are visible in two dimensions. The estimates obtained on the base of pseudo-ε{lunate} expansions originating from the 5-loop 2D RG series are also discussed.

AB - An overview is given of the results obtained recently in the course of renormalization-group (RG) study of two-dimensional (2D) models. RG functions of the two-dimensional n-vector λφ4 Euclidean field theory are written down up to the five-loop terms and perturbative series are resummed by the Padé - Borel - Leroy techniques. An account for the five-loop term is shown to shift the Wilson fixed point only briefly, leaving it outside the segment formed by the results of the lattice calculations. This is argued to reflect the influence of the non-analytical contribution to the β-function. The evaluation of the critical exponents for n = 1, n = 0 and n = - 1 in the five-loop approximation and comparison of the results with known exact values confirm the conclusion that non-analytical contributions are visible in two dimensions. The estimates obtained on the base of pseudo-ε{lunate} expansions originating from the 5-loop 2D RG series are also discussed.

KW - Critical exponents

KW - Five-loop expansions

KW - Ising and n-vector models

KW - Pseudo-ε expansion

KW - Renormalization group

KW - Sextic effective coupling

UR - http://www.scopus.com/inward/record.url?scp=43349085166&partnerID=8YFLogxK

M3 - Review article

AN - SCOPUS:43349085166

VL - 10

SP - 351

EP - 357

JO - Journal of Physical Studies

JF - Journal of Physical Studies

SN - 1027-4642

IS - 4

ER -

ID: 36748976