A classical large N hierarchical vector model in three dimensions: A nonzero fixed point and canonical decay of correlation functions

1998 ◽  
Vol 39 (3) ◽  
pp. 1501-1516
Author(s):  
P. A. Faria da Veiga ◽  
M. O’Carroll ◽  
R. Schor
Keyword(s):  
Fixed Point ◽  
Correlation Functions ◽  
Three Dimensions ◽  
Vector Model ◽  
Large N

scholarly journals The cubic fixed point at large N

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Damon J. Binder
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Ising Model ◽  
Ising Models ◽  
Three Dimensions ◽  
Renormalization Group Flow ◽  
Conformal Bootstrap ◽  
Large N ◽  
Group Flow ◽  
3D Ising Model

Abstract By considering the renormalization group flow between N coupled Ising models in the UV and the cubic fixed point in the IR, we study the large N behavior of the cubic fixed points in three dimensions. We derive a diagrammatic expansion for the 1/N corrections to correlation functions. Leading large N corrections to conformal dimensions at the cubic fixed point are then evaluated using numeric conformal bootstrap data for the 3d Ising model.

scholarly journals 3d large $N$ vector models at the boundary

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Lorenzo Di Pietro ◽  
Edoardo Lauria ◽  
Pierluigi Niro
Keyword(s):  
Fixed Point ◽  
Weak Coupling ◽  
Vector Model ◽  
Boundary Theory ◽  
Weak Duality ◽  
Renormalization Group Flow ◽  
Boundary Interaction ◽  
Large N ◽  
Group Flow ◽  
N Vector

We consider a 4d scalar field coupled to large NN free or critical O(N)O(N) vector models, either bosonic or fermionic, on a 3d boundary. We compute the \betaβ function of the classically marginal bulk/boundary interaction at the first non-trivial order in the large NN expansion and exactly in the coupling. Starting with the free (critical) vector model at weak coupling, we find a fixed point at infinite coupling in which the boundary theory is the critical (free) vector model and the bulk decouples. We show that a strong/weak duality relates one description of the renormalization group flow to another one in which the free and the critical vector models are exchanged. We then consider the theory with an additional Maxwell field in the bulk, which also gives decoupling limits with gauged vector models on the boundary.

scholarly journals RENORMALIZATION GROUP FLOW EQUATIONS FOR THE SCALAR O(N) THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 2119-2124 ◽  
Author(s):  
B.-J. SCHAEFER ◽  
O. BOHR ◽  
J. WAMBACH
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Three Dimensions ◽  
Leading Order ◽  
Renormalization Group Flow ◽  
Derivative Expansion ◽  
Scalar Theory ◽  
Flow Equations ◽  
Self Consistent ◽  
Group Flow

Self-consistent new renormalization group flow equations for an O(N)-symmetric scalar theory are approximated in next-to-leading order of the derivative expansion. The Wilson-Fisher fixed point in three dimensions is analyzed in detail and various critical exponents are calculated.

scholarly journals On the Measure-Preserving Mappings with Three-Dimensions

1993 ◽  
Vol 132 ◽  
pp. 73-89
Author(s):  
Yi-Sui Sun
Keyword(s):  
Fixed Point ◽  
Invariant Manifolds ◽  
Three Dimensional ◽  
Invariant Curve ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Kolmogorov Entropy ◽  
Numerical Exploration ◽  
Area Preserving ◽  
Dimensional Mapping

AbstractWe have systematically made the numerical exploration about the perturbation extension of area-preserving mappings to three-dimensional ones, in which the fixed points of area preserving are elliptic, parabolic or hyperbolic respectively. It has been observed that: (i) the invariant manifolds in the vicinity of the fixed point generally don’t exist (ii) when the invariant curve of original two-dimensional mapping exists the invariant tubes do also in the neighbourhood of the invariant curve (iii) for the perturbation extension of area-preserving mapping the invariant manifolds can only be generated in the subset of the invariant manifolds of original two-dimensional mapping, (iv) for the perturbation extension of area preserving mappings with hyperbolic or parabolic fixed point the ordered region near and far from the invariant curve will be destroyed by perturbation more easily than the other one, This is a result different from the case with the elliptic fixed point. In the latter the ordered region near invariant curve is solid. Some of the results have been demonstrated exactly.Finally we have discussed the Kolmogorov Entropy of the mappings and studied some applications.

scholarly journals N-body Simulations to Test the Reliability of Two-point Correlation Functions of Galaxies

1992 ◽  
Vol 9 ◽  
pp. 703-704
Author(s):  
Yasushi Suto
Keyword(s):  
Correlation Functions ◽  
Large Scale ◽  
Sample Volume ◽  
Limited Data ◽  
Observable Universe ◽  
Large N ◽  
The Galaxy ◽  
Point Correlation ◽  
Systematic Biases ◽  
Redshift Survey

The shape and amplitude of the galaxy – galaxy correlation functions, ξgg(r), are among the most widely used measures of the large-scale structure in the universe (Totsuji & Kihara 1969). The estimates, however, might be seriously affected by the limited size of the sample volume, or equivalently, the limited number of available galaxies. In fact, while the observable universe extends c/H0 ~ 3000h-1Mpc, most observational works to map the distribution of galaxies so far have been mainly applied to samples within ~ 100h-1Mpc from us. Thus a CfA redshift survey slice, for example, of 8h < α < 17h, 26.5° < δ < 32.5°, and cz ≾ 15000km/sec (de Lapparent et al. 1986, 1988) represents merely ~ 2 x 10-5 of the total volume of the observable universe. This clearly illustrates the importance of examining possible systematic biases and variations in the estimates of two-point correlation functions from instrinsically limited data. We studied such sample-to-sample variations by analysing subsamples extracted from large N-body simulation data.

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