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

摘要

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