Upper and lower critical decay exponents of Ising ferromagnet with long-range interaction
Upper and lower critical decay exponents of Ising ferromagnet with long-range interaction
复制标题
长程相互作用伊辛铁磁体的上下临界衰变指数
DOI：
10.1103/physreve.95.012143
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Synge Todo
中科院分区：
文献类型：
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作者：
Toshiki Horita;Hidemaro Suwa;Synge Todo
本文用有序群算法MonteCarlo方法研究了具有代数衰减铁磁长程相互作用的二维Ising模型有限温度相变的普适类，其中（=2）是系统的维数，（= 2）是衰减指数.特别是，我们专注于上，下临界衰变指数，平均场的普遍性，中间和短程的普遍性制度之间的边界。在临界衰减指数，它被发现，在临界温度下的磁化强度的标准Binder比表现出非常缓慢的收敛作为系统尺寸的函数。我们提出了更有效的物理量，即结合Binder比和自结合Binder比，这两者都取消了传统Binder比的有限尺寸修正。利用这些技术，我们清楚地证明了在二维情况下，下临界和上临界衰变指数分别为和7/4，与最近的Monte Carlo和重整化群研究相反[M. Picco，arXiv：1207.1018; T.布兰查德，欧罗巴。Lett. 101，56003（2013）EULEEJ0295-507510.1209/0295-5075/101/56003]。
We investigate the universality class of the finite-temperature phase transition of the two-dimensional Ising model with the algebraically decaying ferromagnetic long-range interaction,, where(=2) is the dimension of the system andis the decay exponent, by means of the order-cluster-algorithm Monte Carlo method. In particular, we focus on the upper and lower critical decay exponents, the boundaries between the mean-field-universality, intermediate, and short-range-universality regimes. At the critical decay exponents, it is found that the standard Binder ratio of magnetization at the critical temperature exhibits extremely slow convergence as a function of the system size. We propose more effective physical quantities, namely the combined Binder ratio and the self-combined Binder ratio, both of which cancel the leading finite-size corrections of the conventional Binder ratio. Utilizing these techniques, we clearly demonstrate that in two dimensions, the lower and upper critical decay exponents areand 7/4, respectively, contrary to the recent Monte Carlo and renormalization-group studies [M. Picco, arXiv:1207.1018; T. Blanchard , Europhys. Lett. 101, 56003 (2013)EULEEJ0295-507510.1209/0295-5075/101/56003].