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Journal of Physics A Mathematical and General

Analytical and non-analytical corrections to finite-size scaling

P Reinicke

Published Oct 21, 1987• 59 citations
Publisher

Abstract

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.
DOI
10.1088/0305-4470/20/15/044

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A method to calculate perturbative corrections to the spectrum of a one-dimensional quantum chain in the scaling variable z is developed from the conformal invariance at its fixed point. Then, from the knowledge of certain correlation functions, one can calculate the first coefficients of the scaling functions. The method is applied successfully to the Ising model, where the corrections are also known from the exact solution. The first coefficients of the magnetic scaling functions of the Ising model are also obtained.
Finite-size corrections to scaling of critical correlation lengths and free energies of Ising and three-state Potts ferromagnets are analysed by numerical methods, on strips of width N sites of square, triangular and honeycomb lattices. Strong evidence is given that the amplitudes of the `analytical' correction terms, N -2 , are identically zero for triangular and honeycomb Ising systems. For Potts spins, our results are broadly consistent with this lattice-dependent pattern of cancellations, though for correlation lengths non-vanishing (albeit rather small) amplitudes cannot be entirely ruled out.
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