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comprehensive study of the Compass Model on the square lattice is performed for the classical and quantum version using Monte-Carlo and Quantum-Monte-Carlo methods. We employ state-of-the-art implementations using Metropolis, Stochastic Series Expansion and Parallel Tempering techniques to obtain the critical ordering temperatures and critical exponents. We gauge and compare our algorithm for the 2D classical case and contrast the influence of special annealed boundary conditions against ordinary periodic
conditions. New systematic results for the quantum model are given which are at odds with a recent Letter [1] on the subject and we
discuss possible reasons for this discrepancy. Our results support a transition in the 2D Ising universality class for both the classical and the quantum model.
[1] T. Tanaka and S. Ishihara, Phys. Rev. Lett. 98, 256402 (2007). |
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