Corner transfer matrices and conformal invariance

1987 ◽  
Vol 69 (2-3) ◽  
pp. 385-391 ◽  
Author(s):  
I. Peschel ◽  
T. T. Truong
Keyword(s):  
Conformal Invariance ◽  
Transfer Matrices ◽  
Corner Transfer Matrices

CONFORMAL PROPERTIES OF CRITICAL ISING MODEL CORNER TRANSFER MATRICES

1990 ◽  
Vol 04 (05) ◽  
pp. 907-912
Author(s):  
Brian DAVIES ◽  
Paul A. PEARCE
Keyword(s):  
Ising Model ◽  
Central Charge ◽  
Finite Size ◽  
Summation Formula ◽  
Transfer Matrices ◽  
Corner Transfer Matrices ◽  
Free Boundary Conditions ◽  
Large N ◽  
Fermion Algebra ◽  
Virasoro Characters

The scaling spectra of finite-size Ising model corner transfer matrices (CTMs) are studied at criticality, using the fermion algebra. The low-lying eigenvalues collapse like 1/ log N for large N as predicted by conformal invariance. The shift in the largest eigenvalue is evaluated analytically using a generalized Euler-Maclaurin summation formula giving πc/6 log N with central charge c=1/2. The spectrum generating functions, for both fixed and free boundary conditions, are expressed simply in terms of the c=1/2 Virasoro characters χ∆(q) with modular parameter q= exp (−π/ log N) and conformal dimensions ∆=0, 1/2, 1/16.

scholarly journals On the Combinatorics of Row and Corner Transfer Matrices of the $A^{(1)}_{n-1}$ Restricted Face Models

1997 ◽  
Vol 12 (20) ◽  
pp. 3551-3586 ◽  
Author(s):  
Srinandan Dasmahapatra
Keyword(s):  
Spectral Data ◽  
Polynomial Identity ◽  
Spin Chain ◽  
Two Dimensional ◽  
Transfer Matrices ◽  
Dimensional Model ◽  
Corner Transfer Matrices ◽  
Weight Lattice ◽  
Index Sets ◽  
Two Dimensional Model

We establish a weight-preserving bijection between the index sets of the spectral data of row-to-row and corner transfer matrices for [Formula: see text] restricted interaction round a face (IRF) models. The evaluation of momenta by adding Takahashi integers in the spin chain language is shown to directly correspond to the computation of the energy of a path on the weight lattice in the two-dimensional model. As a consequence we derive fermionic forms of polynomial analogs of branching functions for the cosets [Formula: see text], and establish a bosonic–fermionic polynomial identity.

THE CORNER TRANSFER MATRIX OF SOME FREE-FERMION SYSTEMS AND MEIXNER’S POLYNOMIALS

1990 ◽  
Vol 04 (05) ◽  
pp. 895-905 ◽  
Author(s):  
T.T. TRUONG ◽  
I. PESCHEL
Keyword(s):  
Asymptotic Behavior ◽  
Orthogonal Polynomials ◽  
Special Class ◽  
Finite Lattice ◽  
Free Fermion ◽  
Transfer Matrices ◽  
Corner Transfer Matrices ◽  
Meixner Polynomials ◽  
Fermion Systems ◽  
Large Lattice

Corner transfer matrices of some free-fermion vertex systems on a finite lattice, are exactly diagonalised in the Hamiltonian limit with the help of a special class of orthogonal polynomials: the Meixner polynomials. We present the derivation, discuss the asymptotic behavior for a large lattice and compare the results with numerical computation.

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