Upper and Lower Critical Decay Exponents of Ising Ferromagnets with Long-range Interaction

Understand

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, $J_{ij} = |\vec{r}_i -\vec{r}_j|^{-(d+\sigma)}$, where $d$ (=2) is the dimension of the system and $\sigma$ 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 critical amplitude of the standard Binder ratio of magnetization exhibits the extremely slow convergence as a function of the system size.
• We propose more effective physical quantities, the combined Binder ratio and the self-combined Binder ratio, both of which cancel the leading finite-size corrections of the conventional Binder ratio.