Abstract
We study the Ising model on the square lattice and show, via numerical simulation, that allowing interactions between spins separated by distances 1 and (two ranges), the critical temperature, , converges monotonically to the critical temperature of the Ising model on as . 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, , and (three ranges), with a multiple of ; in this case our results indicate that converges to the critical temperature of the model on . For percolation, analogous results were proven for the critical probability [B. N. B. de Lima, R. P. Sanchis, and R. W. C. Silva, Stochast. Process. Appl. 121, 2043 (2011)].
- Received 29 October 2019
- Revised 24 March 2020
- Accepted 1 May 2020
DOI:https://doi.org/10.1103/PhysRevE.101.052138
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