• DOI:10.1103/PhysRevE.95.012143
• Corpus ID: 24415913

Upper and lower critical decay exponents of Ising ferromagnets with long-range interaction.

@article{Horita2016UpperAL,
  title={Upper and lower critical decay exponents of Ising ferromagnets with long-range interaction.},
  author={Toshiki Horita and Hidemaro Suwa and Synge Todo},
  journal={Physical review. E},
  year={2016},
  volume={95 1-1},
  pages={
          012143
        }
}

• Toshiki Horita, H. Suwa, S. Todo
• Published 31 May 2016
• Physics
• Physical review. E

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, J_{ij}=|r[over ⃗]_{i}-r[over ⃗]_{j}|^{-(d+σ)}, where d (=2) is the dimension of the system and σ is the decay exponent, by means of the order-N 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 are σ=1 and 7/4, respectively, contrary to the recent Monte Carlo and renormalization-group studies [M. Picco, arXiv:1207.1018; T. Blanchard et al., Europhys. Lett. 101, 56003 (2013)EULEEJ0295-507510.1209/0295-5075/101/56003].