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Multirange Ising model on the square lattice

Published: 26 May 2020

Abstract: We study the Ising model on the square lattice (Z2) and show, via numerical simulation, that allowing interactions between spins separated by distances 1 and m (two ranges), the critical temperature, Tc(m), converges monotonically to the critical temperature of the Ising model on Z4 as m→∞. Only interactions between spins located in directions parallel to each coordinate axis are considered. We also simulated the model with interactions between spins at distances of 1, m, and u (three ranges), with u a multiple of m; in this case our results indicate that Tc(m,u) converges to the critical temperature of the model on Z6. For percolation, analogous results were proven for the critical probability pc [B. N. B. de Lima, R. P. Sanchis, and R. W. C. Silva, Stochast. Process. Appl. 121, 2043 (2011)].
Keywords: numerical simulation / lattice / Ising model / Sanchis / Stochast / axis / coordinate / monotonically

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