Relation of conformal field theory and deformation theory for the Ising model

1987 ◽  
Vol 285 ◽  
pp. 279-294 ◽  
Author(s):  
Barry M. McCoy ◽  
Jacques H.H. Perk
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Ising Model ◽  
Deformation Theory ◽  
Conformal Field

Superuniversal Critical Behavior in Two-Dimensional Random Anisotropic Models with Discrete Symmetries

1998 ◽  
Vol 12 (12n13) ◽  
pp. 1301-1309
Author(s):  
G. Jug ◽  
B. N. Shalaev
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Ising Model ◽  
Critical Behavior ◽  
Quenched Disorder ◽  
Two Dimensional ◽  
Anisotropic Models ◽  
Conformal Field ◽  
Logarithmic Corrections ◽  
Anisotropic Systems

We study the critical behavior of two-dimensional (2D) anisotropic systems with weak quenched disorder described by the Ising model (IM) with random bonds, the dilute N-color Ashkin–Teller model (ATM) and some its generalizations. It is shown that all these models exhibit the same critical behavior as that of the 2D-IM apart from some logarithmic corrections. The minimal conformal field theory (CFT) models with randomness are found to be described by critical exponents which are numerically very close to those of the pure 2D-IM.

HIGHER SPIN SYMMETRY AND SU(2) WZNW MODEL

1994 ◽  
Vol 09 (26) ◽  
pp. 2389-2398
Author(s):  
SASANKA GHOSH
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Ising Model ◽  
Higher Spin Symmetry ◽  
Symmetry Algebra ◽  
Spin Symmetry ◽  
Conformal Field ◽  
Large N ◽  
Wznw Model ◽  
Higher Spin

Generators of an infinite number of conserved charges of the integrable SU(2) WZNW model are identified with the generators of a W1+∞ symmetry algebra. This integrable conformal field theory also describes the ZN symmetric Ising model at the critical point in the large-N limit.

scholarly journals DISORDERED SYSTEMS AND LOGARITHMIC CONFORMAL FIELD THEORY

2003 ◽  
Vol 18 (25) ◽  
pp. 4703-4745 ◽  
Author(s):  
M. REZA RAHIMI TABAR
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Ising Model ◽  
Correlation Functions ◽  
Disordered Systems ◽  
Theoretical Understanding ◽  
Conformal Field ◽  
Logarithmic Conformal Field Theory ◽  
Dilatation Operator ◽  
Logarithmic Singularities

We review a recent development in theoretical understanding of the quenched averaged correlation functions of disordered systems and the logarithmic conformal field theory (LCFT) in d-dimensions. The logarithmic conformal field theory is the generalization of the conformal field theory when the dilatation operator is not diagonal and has the Jordan form. It is discussed that at the random fixed point the disordered systems such as random-bond Ising model, Polymer chain, etc. are described by LCFT and their correlation functions have logarithmic singularities. As an example we discuss in detail the application of LCFT to the problem of random-bond Ising model in 2≤d≤4.

scholarly journals STRUCTURE CONSTANT OF THE YANG–LEE EDGE SINGULARITY

2008 ◽  
Vol 22 (27) ◽  
pp. 4793-4797
Author(s):  
TOMASZ WYDRO ◽  
JOHN F. McCABE
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Ising Model ◽  
Transfer Matrix ◽  
Finite Size ◽  
Structure Constant ◽  
Finite Size Scaling ◽  
Edge Singularity ◽  
Conformal Field ◽  
Size Scaling

This paper studies the Yang–Lee singularity of the 2-dimensional Ising model on the cylinder via transfer matrix and finite-size scaling techniques. These techniques enable a measurement of the 2-point and 3-point correlations and a comparison of a measurement of a corresponding universal amplitude with a prediction for the amplitude from the (A4, A1) minimal conformal field theory.

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

scholarly journals THE FREE FIELD REPRESENTATION OF SU(3) CONFORMAL FIELD THEORY

1993 ◽  
Vol 08 (23) ◽  
pp. 4031-4053
Author(s):  
HOVIK D. TOOMASSIAN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Free Field ◽  
Field Representation ◽  
Conformal Field ◽  
Point Correlation

The structure of the free field representation and some four-point correlation functions of the SU(3) conformal field theory are considered.

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