Efficient Monte Carlo Algorithm in Quasi-One-Dimensional Ising Spin Systems

We develop an efficient Monte Carlo algorithm, which accelerates slow Monte Carlo dynamics in quasi-one-dimensional Ising spin systems. The loop algorithm of the quantum Monte Carlo method is applied to the classical spin models with highly anisotropic exchange interactions. Both correlation time and real CPU time are reduced drastically. The algorithm is demonstrated in the layered triangular-lattice antiferromagnetic Ising model. We have obtained the relation between the transition temperature and the exchange interaction parameters, which modifies the result of the chain-mean-field theory.

Figure 1

The updating procedure of the continuous $c$ axis version. Black (white) rectangles depict the up-state (down-state) spin clusters. The new-generated cluster edges are depicted by broken horizontal lines. Brackets depict the clusters to be updated. We update each cluster state independently using the probability $p_I$.

Figure 2

The relaxation function of the structure factors, $f_{1/3}^2$ and $9f_1^2$, when the simulations start from the ferrimagnetic state (lines) and the PD state (symbols).

Figure 3

Relation between the exchange interaction parameters and the transition temperature $T_{\mathrm{N}1}$ obtained by the Monte Carlo simulation. Arrows depict the point where $|J_2|=|J_1|/2$ for each choice of $J_2/J_c$. The numerical results fall onto the single function as long as $|J_2|<|J_1|/2$.