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The Critical Behavior of 1-dimensional Spin System with Infinite Long-range Interaction Compensating the Effect of Lattice Dimensionality

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概要 By using the Monte Carlo simulation, we investigate the critical behavior of the 1-dimensional spin system with infinite long-range (LR) interaction r^{-(1+σ)}. By changing the value σ, we compare the results with those of the d-dimensional spin system with the nearest-neighbor(NN) interaction only. In the case of XY spin model, we obtain three different type phase transitions, i.e. the mean field type for 0 < σ < 0.5 , the σ-dependent non-trivial one for 0.5 < σ < 1 and 'Berezinskii-Kosterlitz-Thouless (BKT)-like’transition at σ = 1 as in the NN model of d > 4 , 2 < d < 4 and d = 2 , respectively. In the case of q-state clock spin model with σ = 1, we also confirm the BKT-like transition together with the similar q-dependence of the critical behavior to that of the 2-dimensional NN model. These results suggest that the infinite long-range interaction can partly compensate the role of the lattice dimensionality by increasing the effective value d from d = 1 to d = 2.

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登録日 2010.02.02
更新日 2015.11.06