Self consistent Ornstein–Zernike approximation compared with exact results for lattice gases in one and two dimensions

1998 ◽  
Vol 108 (21) ◽  
pp. 8830-8837 ◽  
Author(s):  
J. S. Ho/ye ◽  
A. Borge
Keyword(s):  
Two Dimensions ◽  
Lattice Gases ◽  
Exact Results ◽  
Self Consistent

scholarly journals DIFFICULTIES OF AN INFRARED EXTENSION OF DIFFERENTIAL RENORMALIZATION

1994 ◽  
Vol 09 (07) ◽  
pp. 1067-1096 ◽  
Author(s):  
L. V. AVDEEV ◽  
D. I. KAZAKOV ◽  
I. N. KONDRASHUK
Keyword(s):  
Perturbation Theory ◽  
Fourier Transformation ◽  
Two Dimensions ◽  
Test Scheme ◽  
Two Dimensional ◽  
Differential Identities ◽  
Feynman Integrals ◽  
Differential Renormalization ◽  
Self Consistent ◽  
Infrared Singularities

We investigate the possibility of generalizing the differential renormalization of D. Z. Freedman, K. Johnson and J. I. Latorre in an invariant fashion to theories with infrared divergencies via an infrared [Formula: see text] operation. Two-dimensional σ models and the four-dimensional ɸ4-theory diagrams with exceptional momenta are used as examples, while dimensional renormalization serves as a test scheme for comparison. We write the basic differential identities of the method simultaneously in co-ordinate and momentum space, introducing two scales which remove ultraviolet and infrared singularities. A consistent set of Fourier-transformation formulae is derived. However, the values for tadpole-type Feynman integrals in higher orders of perturbation theory prove to be ambiguous, depending on the order of evaluation of the subgraphs. In two dimensions, even earlier than this ambiguity manifests itself, renormalization-group calculations based on the infrared extension of differential renormalization lead to incorrect results. We conclude that the procedure of extended differential renormalization does not perform the infrared [Formula: see text] operation in a self-consistent way.

Exact Results for Curvature-Driven Coarsening in Two Dimensions

2007 ◽  
Vol 98 (14) ◽  
Author(s):  
Jeferson J. Arenzon ◽  
Alan J. Bray ◽  
Leticia F. Cugliandolo ◽  
Alberto Sicilia
Keyword(s):  
Two Dimensions ◽  
Exact Results ◽  
Curvature Driven

Exact results for the Potts model in two dimensions

1978 ◽  
Vol 19 (6) ◽  
pp. 623-632 ◽  
Author(s):  
A. Hintermann ◽  
H. Kunz ◽  
F. Y. Wu
Keyword(s):  
Potts Model ◽  
Two Dimensions ◽  
Exact Results
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