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

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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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Kyushu Univ. Production Kyushu Univ. Production
Responsibility:
Takamoto, Masahiro(Department of Applied Quantum Physics and Nuclear Engineering, Faculty of Engineering, Kyushu University : Graduate Student)
Muraoka, Yoshinori(Department of General Education, Ariake National College of Technology : Professor)
Idogaki, Toshihiro(Department of Applied Quantum Physics and Nuclear Engineering, Faculty of Engineering, Kyushu University : Professor)

高本, 雅裕(九州大学大学院工学府エネルギー量子工学専攻)
村岡, 良紀(有明工業高等専門学校一般教育科)
井戸垣, 俊弘(九州大学大学院工学研究院エネルギー量子工学部門)

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Language:
English
Publication info:
Memoirs of the Faculty of Engineering, Kyushu University. 69, (4), pp. 187-202, 2009-12-21. Faculty of Engineering, Kyushu University
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Abstract:
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. Read more
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