## Dipolar interaction in a 1-D Ising ring

### Abstract

The effects of a long-range interaction in a one-dimensional (1D) magnetic ring is studied. In this work, the Monte Carlo method is employed to obtain the equilibrium state of a modified quasi-1D Ising model having a dipolar interaction in a ring geometry. At low temperatures (

*T*), the behavior of the magnetization (*M*) as a function of*T*is shown to depend on the strength of the dipolar interaction*(G)*. For a ring consisting of 10 spins, ferromagnetic states occur in the ground state (*T*=0) for a small value of*G*. Antiferromagnetic states are favored when*G*is large even at a finite temperature. The magnetization saturates at high*T*. Also, an effective lowering of the total energy is achieved when smaller values of*G*approach zero and when large value of*G*is increased further. Similar effects are observed for rings having a larger number of spins.