Testing boundary conditions efficiency in simulations of long-range interacting magnetic models

TL;DR

This study compares the effects of different periodic boundary conditions on finite size effects in simulations of long-range magnetic models, revealing when these effects are significantly different.

Contribution

It provides a systematic comparison of first image and full infinite boundary conditions in long-range magnetic systems, highlighting their impact on finite size effects.

Findings

No significant difference in finite size effects when low temperature phase has zero magnetization.

Finite size effects depend on the ratio α/d in ferromagnetic phases.

First image boundary condition induces stronger finite size effects in the classical regime α/d ≤ 3/2.

Abstract

Periodic boundary conditions have not a unique implementation in magnetic systems where all spins interact with each other through a power law decaying interaction of the form $1/r^\alpha$, $r$ being the distance between spins. In this work we present a comparative study of the finite size effects oberved in numerical simulations by using first image convention and full infinite of periodic boundary conditions in one and two-dimensional spin systems with those type of interactions, including the ferromagnetic, antiferromagnetic and competitive interactions cases. Our results show no significative differences between the finite size effects produced by both types of boundary conditions when the low temperature phase has zero global magnetization, while it depends on the ratio $\alpha/d$ for systems with a low temperature ferromagnetic phase. In the last case the first image convention gives much more stronger finite size effects than the other when the system enters into the classical regime $\alpha/d \leq 3/2$.