Corner transfer matrices of the eight-vertex model. II. The Ising model case

1977 ◽  
Vol 17 (1) ◽  
pp. 1-14 ◽  
Author(s):  
R. J. Baxter
Keyword(s):  
Ising Model ◽  
Vertex Model ◽  
Transfer Matrices ◽  
Model Case ◽  
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 CORNER TRANSFER MATRICES AND QUANTUM AFFINE ALGEBRAS

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 279-302 ◽  
Author(s):  
OMAR FODA ◽  
TETSUJI MIWA
Keyword(s):  
Irreducible Representation ◽  
Tensor Product ◽  
Lie Algebra ◽  
Transfer Matrix ◽  
Vertex Model ◽  
Transfer Matrices ◽  
Corner Transfer Matrices ◽  
Quantum Affine Algebras ◽  
Dimensional Irreducible Representation ◽  
Level 1

Let ℋ be the corner-transfer-matrix Hamiltonian for the six-vertex model in the anti-ferroelectric regime. It acts on the infinite tensor product W=V⊗V⊗V⊗⋯, where V is the 2-dimensional irreducible representation of the quantum affine Lie algebra [Formula: see text]. We observe that ℋ is the derivation of [Formula: see text], and conjecture that the eigenvectors of ℋ form the level-1 vacuum representation of [Formula: see text]. We report on checks in support of our conjecture.

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