The Kosterlitz-Thouless universality class |
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| Institution: | 1. Proton Beam Therapy Center, Hokkaido University Hospital, North14 West5, Kita-ku, Sapporo, Hokkaido 060-8638, Japan;2. Department of Medical Physics, Graduate School of Medicine, Hokkaido University, North15 West7, Kita-ku, Sapporo, Hokkaido 060-8638, Japan;3. Global Station of Quantum Medical Science and Engineering, Global Institution for Collaborative Research and Education, Hokkaido University, North15 West7, Kita-ku, Sapporo, Hokkaido 060-8638, Japan;4. Division of Quantum Science and Engineering, Faculty of Engineering, Hokkaido University, North13 West8, Kita-ku, Sapporo, Hokkaido 060-8638, Japan;5. Hitachi Ltd., 1-1 7-chome, Oomika-cho, Hitachi-shi, Ibaraki 319-1292, Japan;1. Department of Engineering Physics, Electronics and Mechanics, Graduate School of Engineering, Nagoya Institute of Technology, Showa-ku, Nagoya 466-8555, Japan;2. Department of Physical Science and Engineering, Graduate School of Engineering, Nagoya Institute of Technology, Showa-ku, Nagoya 466-8555, Japan;3. Department of Chemistry, Graduate School of Science, Hiroshima University, Higashihiroshima, Hiroshima 739-8526, Japan |
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| Abstract: | We examine the Kosterlitz-Thouless universality class and show that essential scaling at this type of phase transition is not self-consistent unless multiplicative logarithmic corrections are included. In the case of specific heat these logarithmic corrections are identified analytically. To identify those corresponding to the susceptibility we set up a numerical method involving the finite-size scaling of Lee-Yang zeroes. We also study the density of zeroes and introduce a new concept called index scaling. We apply the method to the XY model and the c]osely related step model in two dimensions. The critical parameters (including logarithmic corrections) of the step model are compatible with those of the XY model indicating that both models belong to the same universality class. This result then raises questions over how a vortex binding scenario can be the driving mechanism for the phase transition. Furthermore, the logarithmic corrections identified numerically by our methods of fitting are not in agreement with the renormalization group predictions of Kosterlitz and Thouless. |
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