Phys. Rev. Lett. 86, 5305–5308 (2001)Criticality in One Dimension with Inverse Square-Law PotentialsReceived 2 February 2001; published in the issue dated 4 June 2001 We demonstrate that the scaled order parameter for ferromagnetic Ising and three-state Potts chains with inverse square interactions exhibits a universal critical jump, in analogy with the superfluid density in helium films. Renormalization-group arguments are combined with numerical simulations of systems containing up to 106 lattice sites to accurately determine the critical properties of these models. In strong contrast with earlier work, compelling quantitative evidence for the Kosterlitz-Thouless–like character of the phase transition is provided. © 2001 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.86.5305
DOI:
10.1103/PhysRevLett.86.5305
PACS:
64.60.Ak, 05.70.Jk, 64.60.Cn, 75.10.Hk
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