Recently it has been found that for several two-dimensional classical models the amplitude of the correlation length of a finite system at a critical point is universal and related to the correlation-function exponent η. Here we propose that for quantum systems the ratios of two such amplitudes are universal and are related to the ratios of the corresponding exponents. This proposition is confirmed numerically for the transverse Ising model for spin S=1/2,1,3/2, and 2. It is used to calculate η in a simplified way.
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Penson et al. (1984) studied this question.
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