Phenomenological renormalization-group calculations for 12- and 16-vertex models on a square lattice

1984 ◽  
Vol 30 (9) ◽  
pp. 5326-5333 ◽  
Author(s):  
J. F. Stilck ◽  
M. J. de Oliveira ◽  
S. R. Salinas
Keyword(s):  
Renormalization Group ◽  
Square Lattice ◽  
Vertex Models ◽  
Phenomenological Renormalization

Phenomenological Renormalization Group and Cluster Approximation

2014 ◽  
Vol 59 (7) ◽  
pp. 655-662
Author(s):  
O. Borisenko ◽  
◽  
V. Chelnokov ◽  
V. Kushnir ◽  
◽  
...  
Keyword(s):  
Renormalization Group ◽  
Cluster Approximation ◽  
Phenomenological Renormalization

TRANSFER-MATRIX STUDY OF NEGATIVE-FUGACITY SINGULARITY OF HARD-CORE LATTICE GAS

1999 ◽  
Vol 10 (04) ◽  
pp. 517-529 ◽  
Author(s):  
SYNGE TODO
Keyword(s):  
Large Scale ◽  
Lattice Gas ◽  
Central Charge ◽  
Hard Core ◽  
Universality Class ◽  
Two Dimensions ◽  
Square Lattice ◽  
Lattice Gas Models ◽  
Renormalization Technique ◽  
Phenomenological Renormalization

A singularity on the negative-fugacity axis of the hard-core lattice gas is investigated in terms of numerical diagonalization of large-scale transfer matrices. For the hard-square lattice gas, the location of the singular point [Formula: see text] and the critical exponent ν are accurately determined by the phenomenological renormalization technique as -0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge c and the dominant scaling dimension xσ are -4.399996(8) and -0.3999996(7), respectively. Similar analyses for other hard-core lattice-gas models in two dimensions are also performed, and it is confirmed that the universality between these models does hold. These results strongly indicate that the present singularity belongs to the same universality class as the Yang–Lee edge singularity.

Fem Based Simulation of Percolation Features of Disordered Heterogeneous Media Elastic Properties

1994 ◽  
Vol 367 ◽  
Author(s):  
S.A. Timan ◽  
V.G. Oshmian
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Monte Carlo ◽  
Critical Exponents ◽  
Heterogeneous Media ◽  
Square Lattice ◽  
Monte Carlo Data ◽  
Disordered System ◽  
Phenomenological Renormalization

AbstractThe mechanical properties of the 2D elastic rigid-nonrigid disordered system in dependence on the concentrations of the rigid phase are studied. The system is constructed on the basis of the square lattice and finite element method (FEM) approximation. The elasticity threshold of the FE system and the critical exponents are detemined by the phenomenological renormalization (PR) of the Monte Carlo data.

General Square Lattice Vertex Models

2019 ◽  
pp. 430-453
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Square Lattice ◽  
Vertex Model ◽  
Transfer Matrices ◽  
Spectral Parameters ◽  
Vertex Models ◽  
Integrable Quantum ◽  
Special Cases ◽  
Mechanical Models ◽  
The One ◽  
Ice Model

Vertex models more general than the ice model are possible and often have physical applications. The square lattice admits the general sixteen-vertex model of which the special cases, the eight- and the six-vertex model, are the most relevant and physically interesting, in particular through their connection to the one-dimensional integrable quantum mechanical models and the Bethe ansatz. This chapter introduces power- ful tools to examine vertex models, including the R- and L-matrices to encode the Boltzmann vertex weights and the monodromy and transfer matrices, which encode the integrability of the vertex models (i.e. that transfer matrices of different spectral parameters commute). This integrability is ultimately expressed in the Yang–Baxter relations.

Sign in / Sign up

Export Citation Format

Share Document