Revisit of 1D Ising model with inverse-square interactions

Xinsheng Ling^1*

¹Physics, Brown University, Providence, USA

* Presenter:Xinsheng Ling, email:xinsheng_ling@brown.edu

I will discuss the unresolved issues in 1D Ising model with inverse-square interactions. We show that for the one-dimensional Ising model with $1/r^2$ interactions, the Anderson-Yuval-Kosterlitz renormalization-group theory predicts a crossing behavior in the squared magnetization $m^2(L,T)$ of a finite-size system. We show that for Monte Carlo simulations to exhibit the predicted finite-size behavior, the choice of the proper periodic boundary conditions is crucial. A finite-size scaling analysis of the modulus susceptibility peaks yields a critical temperature $T_{c}=1.560(6)$, consistent with the theoretical value $T_{c}=1.563$ found using the Anderson-Yuval-Kosterlitz renormalization-group theory.

Keywords: topological defects, Anderson-Yuval-Kosterlitz RG, Monte Carlo simulations, finite-size scaling