Continuum limits and exact finite-size-scaling functions for one-dimensionalO(N)-invariant spin models |
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Authors: | Attilio Cucchieri Tereza Mendes Andrea Pelissetto Alan D Sokal |
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Institution: | (1) Department of Physics, New York University, 10003 New York, New York;(2) Dipartimento di Fisica, Università degli Studi di Pisa, 56100 Pisa, Italy |
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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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Keywords: | One-dimensional -model" target="_blank">gif" alt="sgr" align="BASELINE" BORDER="0">-model N-vector model RP
N– 1 model mixed isovector/isotensor model continuum limit universality classes finite-size scaling hyperspherical harmonics |
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