Numerical simulation of the XY-model on a two-dimensional random lattice |
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| Affiliation: | 1. Department of Computer Science, Faculty of Physical and Mathematical Sciences, University of Chile, Chile;2. Astronomy Department, Faculty of Physical and Mathematical Sciences, University of Chile, Chile;1. LAPTH, Université Savoie Mont Blanc, CNRS, B.P.110, F-74941 Annecy-le-Vieux Cedex, France;2. Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, 53 Avenue des Martyrs, F-38026 Grenoble, France;3. Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119992, Russia;1. Physics Department, Herbert H. Lehman College and Graduate School, The City University of New York, 250 Bedford Park Boulevard West, Bronx, NY 10468-1589, USA;2. Physical Science and Engineering Division (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia |
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| Abstract: | We discuss a numerical simulation of the planar XY-model on a two-dimensional random lattice. Results obtained on the random lattice are compared with those obtained using identical methods on a square lattice, which acts as a “control experiment”. Calculations were made of the average energy per spin, susceptibility per spin and magnetization. The specific heat was obtained by a numerical differentiation of the energy curve. Also, the number of positive (or negative) spin vortices in the system at different temperatures was calculated. Particular attention is paid to the way in which these vortices entered the system, since it is their appearance which signals the phase transition. Numerical results computed at high temperatures are compared with the theoretical values obtained from high-temperature expansions; and those computed at low temperatures, with the results of spin-wave theory. We investigate the effect of varying the weights for the field theory on the random lattice. |
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