We use Monte Carlo simulations to study the XXZ Heisenberg antiferromagnet in a field in order to clearly determine the nature of the multicritical point. We use a hybrid sampling method with Metropolis and Wolff-cluster algorithms, along with histogram reweighting techniques. Staggered magnetization susceptibilities, Binder cumulants, and finite-size scaling are considered in an effort to detect a possible biconical phase. An analysis of the probability distribution of the magnetization allowed us to conclude that the multicritical point is bicritical and it is in the three-dimensional Heisenberg universality class.We use Monte Carlo simulations to study the XXZ Heisenberg antiferromagnet in a field in order to clearly determine the nature of the multicritical point. We use a hybrid sampling method with Metropolis and Wolff-cluster algorithms, along with histogram reweighting techniques. Staggered magnetization susceptibilities, Binder cumulants, and finite-size scaling are considered in an effort to detect a possible biconical phase. An analysis of the probability distribution of the magnetization allowed us to conclude that the multicritical point is bicritical and it is in the three-dimensional Heisenberg universality class.

Physical Review EMar 17, 20146 citations

Spontaneous magnetization of the XXZ Heisenberg - chain

A.G. Izergin, N Kitanine, Jean Michel Maillet +1 more

arXiv:solv-int/9812021Nuclear Physics BAug 1, 199975 citations

Effects of edges inS=1 Heisenberg antiferromagnetic chains

Seiji Miyashita, Shoji Yamamoto

Properties of the ground state of open chains of the S=1 Heisenberg antiferromagnet are studied by a quantum Monte Carlo method. Size (length) dependences of the ground-state energy, the energy gap, the staggered magnetization 〈 ${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$ 〉 and the spin-correlation function 〈 ${\mathit{S}}_{1}^{\mathit{z}}$ ${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$ 〉 are investigated under free, fixed, and periodic boundary conditions. The size dependences are significant in chains with less than 25 spins, where the magnitude of the staggered magnetization is rather large. However, the fourfold degeneracy of the ground state and the exponential decay of correlations that are inherent to the Haldane system are recovered when the chain length becomes long enough. Both the staggered magnetization and the spin-correlation function decay exponentially. The correlation length is about six in lattice spacing, which agrees with the value obtained in the bulk.Properties of the ground state of open chains of the S=1 Heisenberg antiferromagnet are studied by a quantum Monte Carlo method. Size (length) dependences of the ground-state energy, the energy gap, the staggered magnetization 〈${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$〉 and the spin-correlation function 〈${\mathit{S}}_{1}^{\mathit{z}}$${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$〉 are investigated under free, fixed, and periodic boundary conditions. The size dependences are significant in chains with less than 25 spins, where the magnitude of the staggered magnetization is rather large. However, the fourfold degeneracy of the ground state and the exponential decay of correlations that are inherent to the Haldane system are recovered when the chain length becomes long enough. Both the staggered magnetization and the spin-correlation function decay exponentially. The correlation length is about six in lattice spacing, which agrees with the value obtained in the bulk.

Physical review. B, Condensed matterJul 1, 1993123 citations

Spin 1 vs Spin 1/2 Antiferromagnetic Chains: The Staggered Magnetization

Daniel Charles Mattis, C. Y. Pan

Springer proceedings in physicsJan 1, 19870 citations

{\mathit{S}}_{\mathit{i}}^{\mathit{z}}

〉 and the spin-correlation function 〈

{\mathit{S}}_{1}^{\mathit{z}}

{\mathit{S}}_{\mathit{i}}^{\mathit{z}}

〉 are investigated under free, fixed, and periodic boundary conditions. The size dependences are significant in chains with less than 25 spins, where the magnitude of the staggered magnetization is rather large. However, the fourfold degeneracy of the ground state and the exponential decay of correlations that are inherent to the Haldane system are recovered when the chain length becomes long enough. Both the staggered magnetization and the spin-correlation function decay exponentially. The correlation length is about six in lattice spacing, which agrees with the value obtained in the bulk.