Journal of Physics A Mathematical and General

Finite-size corrections to matrix elements in a conformal theory. Applications to the magnetisation of the three-state Potts model

P Reinicke, T.T. Vescan

Published Jul 11, 1987• 2 citations

Abstract

Using conformal invariance the authors calculate the leading corrections in 1/N to the magnetisation of the three-state Potts quantum chain. The results are in good agreement with the numerical finite-size results.

DOI: 10.1088/0305-4470/20/10/006

Related papers

Analytical and non-analytical corrections to finite-size scaling

P Reinicke

Using conformal invariance the author calculates finite-size corrections to the scaled spectra of one-dimensional quantum chains at the critical point. An explicit application to the Ising and three-state Potts model gives good agreement with analytical and numerical results, respectively.

Journal of Physics A Mathematical and GeneralOct 21, 198759 citations

Finite-size corrections for spin-S Heisenberg chains and conformal properties

B -D Dorfel

The author compares recent results on finite-size corrections for the isotropic (XXX) Heisenberg chain (and its integrable generalisations) with former numerical and analytic calculations. For the ground state and its lowest excitations, leading and non-leading terms are considered. The analysis confirms the predictions of conformal invariance and sheds some new light on the fine structure of finite-size corrections.

Journal of Physics A Mathematical and GeneralJul 7, 19898 citations

Magnetisations from finite-size scaling

Chris J. Hamer

A method of obtaining the spontaneous magnetisation from finite-lattice matrix elements of the magnetic field operator, due to Yang (1952) and Uzelac (1980), is discussed. The method is demonstrated for the case of the Ising model in (1+1) dimensions, and is shown to provide smooth and rapidly convergent finite-lattice sequences. Applied to the case of the three-state Potts (Z 3 ) model in (1+1) dimensions, the method yields an estimate beta =0.111 09+or-0.000 05 for the critical exponent. This confirms Alexander's conjecture of universality with the hard hexagonal model.

Journal of Physics A Mathematical and GeneralDec 1, 198225 citations

Conformal invariance and finite one-dimensional quantum chains

G von Gehlen, V. Rittenberg, H. Ruegg

Based on previous work of Cardy (1984), the authors show in a systematic way how using conformal invariance one can determine the anomalous dimensions of various operators from finite quantum chains with different boundary conditions. The method is illustrated in the case of the three- and four-state Potts models where the anomalous dimensions of the para-fermionic operators are found.

Journal of Physics A Mathematical and GeneralJan 11, 1986117 citations

Logarithmic corrections to finite-size scaling in strips

John Cardy

The corrections to the finite-size scaling behaviour of the eigenvalues of the transfer matrix of a critical theory defined on an infinitely long strip of finite width, which occur when the Hamiltonian contains a marginal operator, are computed using conformal invariance. They show a calculable universal logarithmic character. For the four-state Potts model they agree with numerical data.

Journal of Physics A Mathematical and GeneralDec 1, 1986185 citations

Conformal invariance and surface critical behaviour of a quantum chain with three-spin interaction

Ferenc Iglói

An Ising model with three-spin interaction is investigated by finite-size scaling applying free boundary conditions. The surface critical properties of the model were determined by conformal invariance. Taking into account logarithmic corrections the surface critical exponents obtained are in accordance with the four-state Potts values.

Journal of Physics A Mathematical and GeneralOct 21, 198722 citations