Three-dimensional spin models are important for understanding real magnetic materials. In this work, we study the phase transition of the spin-half (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$S=1/2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mo>=</mo> <mn>1</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>) antiferromagnetic quantum XXZ model with in-plane ferromagnetic interaction in three dimensions. The newly developed worm algorithm allows us to simulate a three-dimensional lattice system up to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$64 \times 64 \times 64$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>64</mn> <mo>×</mo> <mn>64</mn> <mo>×</mo> <mn>64</mn> </mrow> </math></EquationSource> </InlineEquation>. We simulated the spin system in the parametric space of temperature (T) and z-directional spin–spin interaction strength (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\Delta $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Δ</mi> </math></EquationSource> </InlineEquation>). A tentative phase diagram is obtained by the finite-size scaling of superfluid stiffness and the analysis of compressibility. We also obtained the correlation-length critical exponent (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\nu $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ν</mi> </math></EquationSource> </InlineEquation>) with finite-size scaling theory and found <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\nu =0.65(3)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ν</mi> <mo>=</mo> <mn>0.65</mn> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, which is consistent with the classical model.

Phase transitions of a three-dimensional spin-half quantum XXZ model: a quantum Monte Carlo study

期刊论文
发表日期：

2026年3月16日

查看全文

Doje Yi,
Ji-Woo Lee

摘要

Three-dimensional spin models are important for understanding real magnetic materials. In this work, we study the phase transition of the spin-half ( $S=1/2$ $S = 1 / 2$ ) antiferromagnetic quantum XXZ model with in-plane ferromagnetic interaction in three dimensions. The newly developed worm algorithm allows us to simulate a three-dimensional lattice system up to $64 \times 64 \times 64$ $64 \times 64 \times 64$ . We simulated the spin system in the parametric space of temperature (T) and z-directional spin–spin interaction strength ( $\Delta $ $Δ$ ). A tentative phase diagram is obtained by the finite-size scaling of superfluid stiffness and the analysis of compressibility. We also obtained the correlation-length critical exponent ( $\nu $ $ν$ ) with finite-size scaling theory and found $\nu =0.65(3)$ $ν = 0.65 (3)$ , which is consistent with the classical model.