27460121
Finite-size corrections and scaling dimensions of solvable lattice models: An analytic method.
A general analytic method for calculating finite-size corrections, central charges, and scaling dimensions of solvable lattice models is presented. The approach is to solve the special functional equations or inversion identities satisfied by the commuting row transfer matrices of these lattice models at criticality. For purposes of illustration, the method is applied to calculate the central charge c=4/5 and leading magnetic scaling dimension x=2/15 of hard hexagons. These numbers are rational due to special values of Rogers dilogarithms.
121032165
Position-Space Renormalization-Group Transformations: Some Proofs and Some Problems
120685444
Conformal invariance and critical spectrum of corner transfer matrices
The finite-size scaling spectra of Ising model corner transfer matrices and their generators are studied at criticality. The generators are diagonalised using fermion algebra. The low-lying eigenvalues, given by the zeros of Meixner polynomials, are equally spaced and collapse like 1/log N for large N as predicted by conformal invariance. The asymptotics are obtained using a generalised Euler-Maclaurin summation formula. The shift in the largest eigenvalue is given analytically as pi c/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 chi Delta (q) with modular parameter q=exp(- pi /log N) and conformal dimensions Delta =0, 1/2, 1/16.
119373192
Solution of functional equations of restricted An−1(1) fused lattice models
Functional equations, in the form of fusion hierarchies, are studied for the transfer matrices of the fused restricted An−1(1) lattice models of Jimbo, Miwa and Okado. Specifically, these equations are solved analytically for the finite-size scaling spectra, central charges and some conformal weights. The results are obtained in terms of Rogers dilogarithm and correspond to coset conformal field theories based on the affine Lie algebra An−1(1) with GKO pair An−1(1) ⊕ An−1(1) ⊃ An−1(1).
31859363
Solvable hierarchy of cyclic solid-on-solid lattice models.
119509489
A Renormalisation group for TCSA
We discuss the errors introduced by level truncation in the study of boundary renormalisation group flows by the Truncated Conformal Space Approach. We show that the TCSA results can have the qualitative form of a sequence of RG flows between different conformal boundary conditions. In the case of a perturbation by the field phi(13), we propose a renormalisation group equation for the coupling constant which predicts a fixed point at a finite value of the TCSA coupling constant and we compare the predictions with data obtained using TBA equations.
28895492
Triton model calculation test of the Bonn W-matrix rank-one approximation.
The rank-one separable part of the {ital W}-matrix representation of the {ital t} matrix for the Malfliet-Tjon I-III nucleon-nucleon potential has been shown to lead to results for the triton binding energy and low-energy ({ital E}{sub lab}{le}50 MeV) nucleon-deuteron scattering that agree well with results for that potential obtained by solving the full local-potential equations. We explore why this prescription appears to work so well for the Malfliet-Tjon I-III model and test it further using the Reid-soft-core spin-singlet interaction, which possesses a very strong short-range repulsion (a stiff core). For this model, a calculation using the rank-one separable part of the {ital W}-matrix representation of the two-body {ital t} matrix overbinds the triton by 25%.
34160947
Separable approximations to energy dependent potentials.
Standard techniques for approximating a given potential with a separable potential are only applicable to energy independent potentials. A method is presented for extending the standard technique to accommodate explicit energy dependence. The approximation leads to a rank N separable t matrix whose on-shell and half-off-shell forms are exact at N selected energies.