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Multicanonical Monte Carlo study and analysis of tails for the order-parameter distribution of the two-dimensional Ising model

R. Hilfer{}^{{1,2}}, B. Biswal{}^{{1,3}}, H.G. Mattutis{}^{{4}}, W. Janke{}^{5}
{}^{1}ICA-1, Universität Stuttgart, Pfaffenwaldring 27, 70569 Stuttgart, Germany
{}^{2}Institut für Physik, Universität Mainz, 55099 Mainz, Germany,
{}^{3}Department of Physics, Sri Venkateswara College, University of Delhi, New Delhi - 110 021, India
{}^{4}Tokyo University of Electro-communications, Dept. of Mechanical and Control Engineering, Chofu, Tokyo 182-8585, Japan
{}^{5}Institut für Theoretische Physik, Universität Leipzig, Augustusplatz 10/11, D-04109 Leipzig, Germany

The tails of the critical order-parameter distribution of the two-dimensional Ising model are investigated through extensive multicanonical Monte Carlo simulation. Results for fixed boundary conditions are reported here, and compared with known results for periodic boundary conditions. Clear numerical evidence for “fat” stretched exponential tails exists below the critical temperature, indicating the possible presence of fat tails at the critical temperature. Our work suggests that the true order parameter distribution at the critical temperature must be considered to be unknown at present.

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PACS number(s): 05.50.+q, 64.60.Cn, 64.60.Fr, 05.70.Ln