Monte Carlo studies of one-dimensional quantum Heisenberg andXYmodels

The Suzuki-Trotter transformation has been used to transform $N$-spin $S=\frac{1}{2}$ Heisenberg and $\mathrm{XY}$ chains into two-dimensional ($N\times 2m$) classical Ising models with complicated interactions. A Monte Carlo method using multispin flipping techniques is then used to study these models for $\frac{\mathrm{kT}}{\mathrm{}\left|J\right|\mathrm{}}\ge 0.0125$ and $m\le 10$. Finite-size scaling is used to analyze the low-temperature susceptibility of the ferromagnetic Heisenberg chain, and we find a power-law divergence $\chi =T^{-\gamma }$ with $\gamma =1.32\mathrm{}\pm 0.13$. Difficulties in the method, particularly due to singular bonding, are discussed.