Simulating graphene impurities using the worm algorithm

TL;DR

This paper employs the worm algorithm to simulate the 2D Ising model and impurity effects on graphene, accurately determining critical temperatures and exploring impurity interactions.

Contribution

It introduces the use of the worm algorithm for simulating impurities on graphene and analyzing their magnetic ordering and critical temperature dependencies.

Findings

High-accuracy calculation of T_C for the 2D Ising model

Demonstration of magnetic ordering of impurities on graphene

Analysis of T_C dependence on interaction constants

Abstract

The two-dimensional Ising model is studied by performing computer simulations with one of the Monte Carlo algorithms - the worm algorithm. The critical temperature T_C of the phase transition is calculated by the usage of the critical exponents and the results are compared to the analytical result, giving a very high accuracy. We also show that the magnetic ordering of impurities distributed on a graphene sheet is possible, by simulating the properly constructed model using the worm algorithm. The value of T_C is estimated. Furthermore, the dependence of T_C on the interaction constants is explored. We outline how one can proceed in investigating this relation in the future.