Verification of a new quantum simulation approach through its application to two-dimensional Ising lattices |
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| Affiliation: | 1. Department of Applied Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China;2. Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 5, 121 16 Prague 2, Czech Republic;1. Donbass State Engineering Academy, Kramatorsk 84313, Ukraine;2. Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia-UdeA, Calle 70 No. 52-21, Medellín, Colombia;3. Escuela de Ingeniería de Antioquia-EIA, Medellín, Colombia;4. Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, CP 62209 Cuernavaca, Morelos, México;5. Institute of Physics, Kyiv 80028, Ukraine;1. Institute of Strength Physics and Materials Science of SB RAS, 2/4 Akademichesky Avenue, Tomsk 634021, Russia;2. V.D. Kuznetsov Siberian Physical Technical Institute of Tomsk State University, 1 Novosobornaja Square, Tomsk 634050, Russia;1. School of Science, Beijing University of Chemical Technology, P.O. Box 26, Beijing 100029, China;2. Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China;3. State Key Laboratory for Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China;1. School of Materials Science and Engineering, Shandong Jianzhu University, Jinan 250101, PR China;2. Beijing Aeronautical Manufacturing Technology Research Institute, Beijing 100024, PR China |
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| Abstract: | A new quantum simulation approach has been applied in the present work to the two-dimensional (2D) ferromagnetic and antiferromagnetic Ising lattices to calculate their magnetic structures, magnetizations, free energies and specific heats in the absence of an external magnetic field. Surprisingly, no size effects could be observed in our simulations performed for the Ising lattices of different sizes. Most importantly, our calculated spontaneous thermally averaged spins for the two kinds of systems are exactly same as those evaluated with quantum mean field theory, and the magnetic structures simulated at all chosen temperatures are perfectly ferromagnetic or antiferromagnetic, verifying the correctness and applicability of our quantum model and computational algorithm. On the other hand, if the classical Monte Carlo (CMC) method is applied to the ferromagnetic 2D Ising lattice with S=1, it is able to generate correct magnetization well consistent with Onsager's theory; but in the case of S=1/2, the computational results of CMC are incomparable to those predicted with the quantum mean field theory, giving rise to very much reduced magnetization and considerably underestimated Curie temperature. The difficulty met by the CMC method is mainly caused by its improperly calculated exchange energy of the randomly selected spin in every simulation step, especially immediately below the transition temperature, where the thermal averages of spins are much less than 1/2, however they are assigned to ±1/2 by CMC to evaluate the exchange energies of the spins, such improper manipulation is obviously impossible to lead the code to converge to the right equilibrium states of the spin systems. |
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| Keywords: | Simulation approach Algorithm Quantum theory Ising model |
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