Critical behavior of Gaussian model on diamond-type hierarchical lattices

1999 ◽  
Vol 42 (3) ◽  
pp. 325-331 ◽  
Author(s):  
Kong Xiangmu ◽  
Li Song
Keyword(s):  
Critical Behavior ◽  
Gaussian Model ◽  
Hierarchical Lattices ◽  
Diamond Type

Family of diamond-type hierarchical lattices

1988 ◽  
Vol 38 (1) ◽  
pp. 728-731 ◽  
Author(s):  
Z. R. Yang
Keyword(s):  
Hierarchical Lattices ◽  
Diamond Type

scholarly journals STAR-MATRIX MODELS

1995 ◽  
Vol 10 (35) ◽  
pp. 2709-2725
Author(s):  
E. VINTELER
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Matrix Models ◽  
Critical Behavior ◽  
Gaussian Model ◽  
Explicit Formulas ◽  
Special Cases ◽  
Q Matrix

The star-matrix models are difficult to solve due to the multiple powers of the Vandermonde determinants in the partition function. We apply to these models a modified Q-matrix aprpoach and we get results consistent with those obtained by other methods. As examples we study the inhomogeneous Gaussian model on Bethe tree and matrix q-Potts-like model. For the last model in the special cases q=2 and q=3, we write down explicit formulas which determine the critical behavior of the system. For q=2 we argue that the critical behavior is indeed that of the Ising model on the ϕ3 lattice.

scholarly journals CONTINUUM LIMITS OF “INDUCED QCD”: LESSONS OF THE GAUSSIAN MODEL AT d=1 AND BEYOND

1993 ◽  
Vol 08 (08) ◽  
pp. 1411-1436 ◽  
Author(s):  
I.I. KOGAN ◽  
A. MOROZOV ◽  
G.W. SEMENOFF ◽  
N. WEISS
Keyword(s):  
Scalar Field ◽  
Critical Behavior ◽  
Scalar Potential ◽  
Mean Field ◽  
Gaussian Model ◽  
Scalar Fields ◽  
Field Analysis ◽  
Mean Field Approximation ◽  
Simple Explanation ◽  
Logarithmic Term

We analyze the scalar field sector of the Kazakov-Migdal model of induced QCD. We present a detailed description of the simplest one-dimensional (d=1) model which supports the hypothesis of wide applicability of the mean-field approximation for the scalar fields and the existence of critical behavior in the model when the scalar action is Gaussian. Despite the occurrence of various nontrivial types of critical behavior in the d=1 model as N→∞, only the conventional large N limit is relevant for its continuum limit. We also give a mean-field analysis of the N=2 model in anyd and show that a saddle point always exists in the region [Formula: see text]. In d=1 it exhibits critical behavior as [Formula: see text]. However when d>1 there is no critical behavior unless non-Gaussian terms are added to the scalar field action. We argue that similar behavior should occur for any finite N thus providing a simple explanation of a recent result of D. Gross. We show that critical behavior at d>1 and [Formula: see text] can be obtained by adding a logarithmic term to the scalar potential. This is equivalent to a local modification of the integration measure in the original Kazakov—Migdal model. Experience from previous studies of the Generalized Kontsevich Model implies that, unlike the inclusion of higher powers in the potential, this minor modification should not substantially alter the behavior of the Gaussian model.

Diamond-type hierarchical lattices for the Potts antiferromagnet

1991 ◽  
Vol 43 (10) ◽  
pp. 8576-8582 ◽  
Author(s):  
Yung Qin ◽  
Z. R. Yang
Keyword(s):  
Hierarchical Lattices ◽  
Diamond Type
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