Finite Size Analysis of the One-dimensional $q = \infty$ Clock Model

Details Finite Size Analysis of the One-dimensional $q = \infty$ Clock Model Finite Size Analysis of the One-dimensional $q = \infty$ Clock Model

1993-05-27

arxiv.org/abs/hep-lat/9305022v1

J.Phys. A27 (1994) 3707-3714

Physics

High Energy Physics

High Energy Physics - Lattice

9 pages + 3 ps figures not included, LaTeX, DFTUZ 93.3

Scientific paper

10.1088/0305-4470/27/11/020

We analyze the finite size scaling of the $q$-state clock model in the $q \rightarrow \infty$ limit. The behaviors of the specific heat, Binder-Landau and U4 cumulants agree with the Borgs-Koteck\'y ans\"atz for first order phase transitions. However, we find that the leading correction to the position of the extremal points of these quantities is not universal. On the other hand, the finite size corrections to the mass gap behave like for second order phase transitions. In particular, the curves corresponding to different size approximations do not cross in the vicinity of the transition points. The feature is associated to the existence of a divergent correlation length and holds for a wider class of models.

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