Abstract
We solve exactly the general one-dimensionalO(N)-invariant spin model taking values in the sphereS N−1, with nearest-neighbor interactions, in finite volume with periodic boundary conditions, by an expansion in hyperspherical harmonics. The possible continuum limits are discussed for a general one-parameter family of interactions and an infinite number of universality classes is found. For these classes we compute the finite-size-scaling functions and the leading corrections to finite-size scaling. A special two-parameter family of interactions (which includes the mixed isovector/isotensor model) is also treated and no additional universality classes appear. In the appendices we give new formulae for the Clebsch-Gordan coefficients and 6−j symbols of theO(N) group, and some new generalizations of the Poisson summation formula; these may be of independent interest.
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Cucchieri, A., Mendes, T., Pelissetto, A. et al. Continuum limits and exact finite-size-scaling functions for one-dimensionalO(N)-invariant spin models. J Stat Phys 86, 581–673 (1997). https://doi.org/10.1007/BF02199114
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DOI: https://doi.org/10.1007/BF02199114