O(n) VECTOR MODEL ON A PLANAR RANDOM LATTICE: SPECTRUM OF ANOMALOUS DIMENSIONS

The O (n) model on a two-dimensional dynamical random lattice is reformulated as a random matrix problem. The critical properties of the model are encoded in the spectral density of the random matrix which satisfies an integral equation with Cauchy kernel. The analysis of its singularities shows that the model can be critical for −2 ≤ n ≤ 2 and allows the determination of the anomalous dimensions of an infinite series of magnetic operators. The results coincide with those found in Ref. 11 for 2d quantum gravity.

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O(n) VECTOR MODEL ON A PLANAR RANDOM LATTICE: SPECTRUM OF ANOMALOUS DIMENSIONS

The Large N Expansion in Quantum Field Theory and Statistical Physics ◽

10.1142/9789814365802_0063 ◽

1993 ◽

pp. 946-955

Author(s):

I. K. KOSTOV

Keyword(s):

Vector Model ◽

Random Lattice ◽

Lattice Spectrum ◽

Anomalous Dimensions ◽

N Vector

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Conformal symmetry and the spectrum of anomalous dimensions in the N-vector model in 4−ϵ dimensions

Nuclear Physics B ◽

10.1016/0550-3213(93)90124-8 ◽

1993 ◽

Vol 402 (3) ◽

pp. 669-692 ◽

Cited By ~ 23

Author(s):

Stefan K. Kehrein ◽

Franz J. Wegner ◽

Yurej M. Pismak

Keyword(s):

Conformal Symmetry ◽

Vector Model ◽

Anomalous Dimensions ◽

N Vector

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The structure of the spectrum of anomalous dimensions in the N-vector model in 4 − ϵ dimensions

Nuclear Physics B ◽

10.1016/0550-3213(94)90406-5 ◽

1994 ◽

Vol 424 (3) ◽

pp. 521-546 ◽

Cited By ~ 16

Author(s):

Stefan K. Kehrein ◽

Franz Wegner

Keyword(s):

Vector Model ◽

Anomalous Dimensions ◽

N Vector

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Critical properties of the two-dimensional Z(5) vector model

10.22323/1.105.0274 ◽

2011 ◽

Author(s):

Gennaro Cortese ◽

Oleg Borisenko ◽

Roberto Fiore ◽

Mario Gravina ◽

Alessandro Papa

Keyword(s):

Vector Model ◽

Two Dimensional ◽

Critical Properties

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Dynamic critical properties of a stochastic n-vector model

Physica A Statistical Mechanics and its Applications ◽

10.1016/0378-4371(77)90166-2 ◽

1977 ◽

Vol 87 (1) ◽

pp. 1-34 ◽

Cited By ~ 15

Author(s):

L. Sasvári ◽

P. Szépfalusy

Keyword(s):

Vector Model ◽

Critical Properties ◽

N Vector

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Comparison between theoretical four-loop predictions and Monte Carlo calculations in the two-dimensional N-vector model for N = 3, 4, 8

Nuclear Physics B - Proceedings Supplements ◽

10.1016/0920-5632(96)00169-7 ◽

1996 ◽

Vol 47 (1-3) ◽

pp. 763-766 ◽

Cited By ~ 10

Author(s):

Sergio Caracciolo ◽

Robert G. Edwards ◽

Tereza Mendes ◽

Andrea Pelissetto ◽

Alan D. Sokal

Keyword(s):

Monte Carlo ◽

Vector Model ◽

Two Dimensional ◽

Monte Carlo Calculations ◽

N Vector

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Critical properties in two-dimensional order-disorder phase transitions: experimental determination of the exponents alpha and eta by integrating methods

EPL (Europhysics Letters) ◽

10.1209/epl/i1997-00220-2 ◽

1997 ◽

Vol 38 (3) ◽

pp. 165-170 ◽

Cited By ~ 1

Author(s):

C Voges ◽

H Pfnür

Keyword(s):

Phase Transitions ◽

Experimental Determination ◽

Two Dimensional ◽

Critical Properties

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ANOMALOUS DIMENSIONS OF SOFT OPERATORS IN SUPERSYMMETRIC NONLINEAR SIGMA-MODELS

Modern Physics Letters A ◽

10.1142/s0217732393003986 ◽

1993 ◽

Vol 08 (40) ◽

pp. 3845-3852

Author(s):

KAY JÖRG WIESE

Keyword(s):

Sigma Models ◽

Wide Class ◽

Vector Model ◽

Supersymmetric Model ◽

Harmonic Polynomials ◽

Loop Order ◽

Anomalous Dimensions ◽

Bosonic Model ◽

N Vector ◽

Nonlinear Sigma Models

The renormalization ζ-function for supersymmetric nonlinear sigma-models is calculated up to three-loop order. For a wide class of models, which includes the N-vector model and matrix models, the result can be summarized as follows: If the ζ-function for the bosonic model is [Formula: see text], then the ζ-function for the supersymmetric model takes the form [Formula: see text]. This is the case for arbitrary harmonic polynomials of the field variables (so called "soft operators").

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