Monte-Carlo Calculation of Quantum J ₁ – J ₂ Model on the Square Lattice

Abstract

We used the modified Decoupled Cell method (mDCM) of quantum Monte Carlo simulation to calculate the thermodynamic properties and spin configurations of the frustrated J ₁ – J ₂ model on the square lattice by increasing the frustration parameter $\alpha = \frac{{{J_2}}}{{{J_1}}}$ from 0 to 1. The size N of a system used in Monte Carlo simulation in this study is 32 × 32. We found that for small values of α the Neel state is a ground state spin configutation of this model system, whereas for α > 0.6 a collinear state is its ground state configuration instead of the Neel state.