scholarly journals Two-Dimensional Critical Percolation: The Full Scaling Limit

2006 ◽  
Vol 268 (1) ◽  
pp. 1-38 ◽  
Author(s):  
Federico Camia ◽  
Charles M. Newman
Keyword(s):  
Scaling Limit ◽  
Two Dimensional ◽  
Critical Percolation

Estimates of critical percolation probabilities for a set of two-dimensional lattices

1972 ◽  
Vol 71 (1) ◽  
pp. 97-106 ◽  
Author(s):  
D. G. Neal
Keyword(s):  
Monte Carlo ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Critical Percolation ◽  
Site Percolation

AbstractThis paper describes new detailed Monte Carlo investigations into bond and site percolation problems on the set of eleven regular and semi-regular (Archimedean) lattices in two dimensions.

scholarly journals SUPERLOOP EQUATIONS AND TWO-DIMENSIONAL SUPERGRAVITY

1992 ◽  
Vol 07 (21) ◽  
pp. 5337-5367 ◽  
Author(s):  
L. ALVAREZ-GAUMÉ ◽  
H. ITOYAMA ◽  
J.L. MAÑES ◽  
A. ZADRA
Keyword(s):  
Partition Function ◽  
Discrete Model ◽  
Continuum Limit ◽  
Basic Assumption ◽  
Scaling Limit ◽  
Integrable Hierarchy ◽  
Two Dimensional ◽  
Virasoro Constraints ◽  
Double Scaling Limit ◽  
The Continuum

We propose a discrete model whose continuum limit reproduces the string susceptibility and the scaling dimensions of (2, 4m) minimal superconformal models coupled to 2D supergravity. The basic assumption in our presentation is a set of super-Virasoro constraints imposed on the partition function. We recover the Neveu-Schwarz and Ramond sectors of the theory, and we are also able to evaluate all planar loop correlation functions in the continuum limit. We find evidence to identify the integrable hierarchy of nonlinear equations describing the double scaling limit as a supersymmetric generalization of KP studied by Rabin.

Ideal chain on a two-dimensional critical percolation cluster

1992 ◽  
Vol 25 (8) ◽  
pp. L461-L468 ◽  
Author(s):  
A Giacometti ◽  
H Nakanishi ◽  
A Maritan ◽  
N H Fuchs
Keyword(s):  
Percolation Cluster ◽  
Two Dimensional ◽  
Critical Percolation ◽  
Ideal Chain

FROM INHOMOGENEOUS SIX-VERTEX LATTICE MODELS TO CONTINUUM QUANTUM INTEGRABLE MODELS

1992 ◽  
Vol 07 (25) ◽  
pp. 6385-6403
Author(s):  
Y.K. ZHOU
Keyword(s):  
Integrable Systems ◽  
Scaling Limit ◽  
Lattice Models ◽  
Integrable Models ◽  
Two Dimensional ◽  
Vertex Model ◽  
Quantum Integrable Systems ◽  
Vertex Models ◽  
Quantum Integrable Models ◽  
Sine Gordon Model

A method to find continuum quantum integrable systems from two-dimensional vertex models is presented. We explain the method with the example where the quantum sine-Gordon model is obtained from an inhomogeneous six-vertex model in its scaling limit. We also show that the method can be applied to other models.

scholarly journals Loop Models, Marginally Rough Interfaces, and the Coulomb Gas

1997 ◽  
Vol 11 (01n02) ◽  
pp. 153-159 ◽  
Author(s):  
Jané Kondev
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Physical Interpretation ◽  
Scaling Limit ◽  
Coarse Graining ◽  
Coulomb Gas ◽  
Effective Field ◽  
Liouville Theory ◽  
Exact Results ◽  
Two Dimensional

We develop a coarse-graining procedure for two-dimensional models of fluctuating loops by mapping them to interface models. The result is an effective field theory for the scaling limit of loop models, which is found to be a Liouville theory with imaginary couplings. This field theory is completely specified by geometry and conformal invariance alone, and it leads to exact results for the critical exponents and the conformal charge of loop models. A physical interpretation of the Dotsenko-Fateev screening charge is found.

scholarly journals DOUBLE SCALING LIMIT OF THE SUPER-VIRASORO CONSTRAINTS

1993 ◽  
Vol 08 (13) ◽  
pp. 2297-2331 ◽  
Author(s):  
L. ALVAREZ-GAUMÉ ◽  
K. BECKER ◽  
M. BECKER ◽  
R. EMPARAN ◽  
J. MAÑES
Keyword(s):  
Scaling Limit ◽  
Majorana Fermion ◽  
Two Dimensional ◽  
Genus Zero ◽  
Heuristic Argument ◽  
Kdv Hierarchy ◽  
Virasoro Constraints ◽  
Bosonic Part ◽  
Double Scaling Limit ◽  
The Continuum

We obtain the double scaling limit of a set of superloop equations recently proposed to describe the coupling of two-dimensional supergravity to minimal superconformal matter of type (2,4m). The continuum loop equations are described in terms of a [Formula: see text] theory with a Z2-twisted scalar field and a Weyl–Majorana fermion in the Ramond sector. We have computed correlation functions in genus zero, one and partially in genus two. An integrable supersymmetric hierarchy describing our model has not yet been found. We present a heuristic argument showing that the purely bosonic part of our model is described by the KdV hierarchy.

UNIVERSALITY OF THE MATRIX MODEL APPROACH TO TWO-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (15) ◽  
pp. 1387-1396
Author(s):  
FREDDY PERMANA ZEN
Keyword(s):  
Quantum Gravity ◽  
Matrix Model ◽  
Scaling Limit ◽  
Numerical Calculations ◽  
Two Dimensional ◽  
Coupled Equations ◽  
The Matrix ◽  
Pure Gravity ◽  
Double Scaling Limit ◽  
Model Approach

Universality with respect to triangulations is investigated in the Hermitian one-matrix model approach to 2-D quantum gravity for a potential containing both even and odd terms, [Formula: see text]. With the use of analytical and numerical calculations, I find that the universality holds and the model describes pure gravity, which leads in the double scaling limit to coupled equations of Painlevé type.

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