The 2D non self-dual Ising lattices: An exact renormalization group treatment

2021 ◽  
pp. 2150170
Author(s):  
Tuncer Kaya
Keyword(s):  
Renormalization Group ◽  
Group Treatment ◽  
Nearest Neighbor ◽  
Pair Correlation ◽  
Exact Expression ◽  
Duality Relation ◽  
Honeycomb Lattice ◽  
Exact Relation ◽  
Triangular Lattices ◽  
Exact Renormalization Group

In this work, an exact renormalization group treatment of honeycomb lattice leading to an exact relation between the coupling strengths of the honeycomb and the triangular lattices is presented. Using the honeycomb and the triangular duality relation, the critical coupling values of honeycomb and triangular lattices are calculated exactly by the simultaneous solution of the renormalized relation and the duality relation, without using the so-called star-triangular transformation. Apparently, the obtained coupling relation is unique. It not only takes place the role of the star triangular relation, but it is also the only exact relation obtained from renormalization group theory other than the 1D Ising chain. An exact pair correlation function expression relating the nearest neighbors and the next nearest neighbor correlation functions are also obtained for the honeycomb lattice. Utilizing this correlation relation, an exact expression of the correlation length of the honeycomb lattice is calculated analytically for the coupling constant values less than the critical value in the realm of the scaling theory. The critical exponents [Formula: see text] and [Formula: see text] are also calculated as [Formula: see text] and [Formula: see text].

scholarly journals FIELD BEHAVIOR OF AN ISING MODEL WITH APERIODIC INTERACTIONS

2000 ◽  
Vol 14 (14) ◽  
pp. 1473-1480
Author(s):  
ANGSULA GHOSH ◽  
T. A. S. HADDAD ◽  
S. R. SALINAS
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Ising Model ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Exchange Interactions ◽  
Universality Class ◽  
Recursion Relations ◽  
Hierarchical Lattices ◽  
Exact Renormalization Group

We derive exact renormalization-group recursion relations for an Ising model, in the presence of external fields, with ferromagnetic nearest-neighbor interactions on Migdal–Kadanoff hierarchical lattices. We consider layered distributions of aperiodic exchange interactions, according to a class of two-letter substitutional sequences. For irrelevant geometric fluctuations, the recursion relations in parameter space display a nontrivial uniform fixed point of hyperbolic character that governs the universal critical behavior. For relevant fluctuations, in agreement with previous work, this fixed point becomes fully unstable, and there appears a two-cycle attractor associated with a new critical universality class.

APPLICATION OF EXACT RENORMALIZATION GROUP TECHNIQUES TO THE NON-PERTURBATIVE STUDY OF SUPERSYMMETRIC FIELD THEORY

2004 ◽  
Vol 18 (04n05) ◽  
pp. 469-478 ◽  
Author(s):  
STEFANO ARNONE ◽  
KENSUKE YOSHIDA
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Renormalization Group Equation ◽  
Group Method ◽  
Group Equation ◽  
Renormalization Group Method ◽  
Exact Relation ◽  
Yang Mills ◽  
Supersymmetric Gauge ◽  
Exact Renormalization Group

A simple form of the exact renormalization group method is proposed for the study of supersymmetric gauge field theory. The method relies on the existence of ultraviolet-finite four dimensional gauge theories with extended supersymmetry. The resulting exact renormalization group equation crucially depends on the Konishi anomaly of N=1 super Yang–Mills. We illustrate our method by dealing with the NSVZ exact relation for the beta functions, the N=2 super Yang–Mills effective potential and the N=1 super Yang–Mills gluon superpotential (the so-called Veneziano–Yankielowicz potential).

scholarly journals EXACT RENORMALIZATION GROUP EQUATION IN THE PRESENCE OF RESCALING ANOMALY II

2002 ◽  
Vol 17 (18) ◽  
pp. 1191-1205 ◽  
Author(s):  
STEFANO ARNONE ◽  
DARIO FRANCIA ◽  
KENSUKE YOSHIDA
Keyword(s):  
Renormalization Group ◽  
Exact Expression ◽  
Flow Equation ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Potential Term ◽  
Yang Mills ◽  
Text Model ◽  
The One ◽  
Exact Renormalization Group

Exact renormalization group techniques are applied to the mass deformed [Formula: see text] super-symmetric Yang–Mills theory, viewed as a regularized [Formula: see text] model. The solution of the flow equation, in case of dominance of the potential term, reproduces the one-loop (perturbatively exact) expression for the effective action of [Formula: see text] supersymmetric Yang–Mills theory, when the regularizing mass, M, reaches the value of the dynamical cutoff Λ. One speculates about the way in which further nonperturbative contributions (instanton effects) may be accounted for.

Exact renormalization group treatment of the piecewise directed random walks on fractals

1988 ◽  
Vol 150 (2) ◽  
pp. 402-418 ◽  
Author(s):  
S. Elezović-Hadžić ◽  
S. Milošević ◽  
H.W. Capel ◽  
G.L. Wiersma
Keyword(s):  
Renormalization Group ◽  
Random Walks ◽  
Group Treatment ◽  
Exact Renormalization Group

Real-space renormalization-group treatment of the Maier-Saupe-Zwanzig model for biaxial nematic structures

2021 ◽  
Vol 103 (3) ◽  
Author(s):  
Cícero T. G. dos Santos ◽  
André P. Vieira ◽  
Silvio R. Salinas ◽  
Roberto F. S. Andrade
Keyword(s):  
Renormalization Group ◽  
Group Treatment ◽  
Real Space ◽  
Real Space Renormalization Group ◽  
Biaxial Nematic

Generalized renormalization group treatment of the growth kinetics of unstable systems

1985 ◽  
Vol 41 (1-2) ◽  
pp. 17-36 ◽  
Author(s):  
Scott R. Anderson ◽  
Gene F. Mazenko ◽  
Oriol T. Valls
Keyword(s):  
Renormalization Group ◽  
Growth Kinetics ◽  
Group Treatment ◽  
Unstable Systems ◽  
Kinetics Of

scholarly journals A MANIFESTLY GAUGE INVARIANT AND UNIVERSAL CALCULUS FORSU(N) YANG–MILLS

2006 ◽  
Vol 21 (23n24) ◽  
pp. 4627-4761 ◽  
Author(s):  
OLIVER J. ROSTEN
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Explicit Dependence ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Group A ◽  
Β Function ◽  
Exact Renormalization Group

Within the framework of the Exact Renormalization Group, a manifestly gauge invariant calculus is constructed for SU (N) Yang–Mills. The methodology is comprehensively illustrated with a proof, to all orders in perturbation theory, that the β function has no explicit dependence on either the seed action or details of the covariantization of the cutoff. The cancellation of these nonuniversal contributions is done in an entirely diagrammatic fashion.

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