发表机构
Instituto Federal de Goiás; Instituto de Física, Universidade Federal de Goiás（戈亚斯联邦理工学院; 戈亚斯联邦大学物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过Wang–Landau方法结合场混合等技术，高分辨率绘制蜂窝晶格Blume–Capel铁磁体的相边界，确定三临界点等参数，得到界面张力指数等结果，揭示其标度行为与三临界伊辛模型相符。
AI 中文摘要
我们对蜂窝晶格（配位数z=3）上的自旋-1 Blume–Capel铁磁体开展了高分辨率数值研究。采用Wang–Landau方法对联合态密度Ω(E₁,E₂)进行估计，并结合场混合技术，绘制了一级相变线，确定了三临界点的坐标为(Δ_t,T_t)=[1.4819(2),0.4022(7)]。对尺寸L=36和48的Metropolis模拟结果进行直方图重权处理，提供了独立的一致性检验，其交叉温度约为0.4039，与Wang–Landau外推结果相符。通过场混合分析得到r=-1.586(19)，而多正则共相线的斜率给出了一致且更精确的估计值r=-1.587(5)。以零温场Δ₀=zJ/2归一化后，蜂窝、正方形、三角形及简单立方晶格的现有r估计值聚集在r/Δ₀≃-1.06附近，其绝对值比平均场值-1大约6%；在所考察的范围内，未观测到其对配位数或维度的系统依赖性。对σ_Q的有限尺寸标度分析给出y_t=1.795(7)，与三临界伊辛值9/5一致，而四阶累积量标度与y_g=4/5相符。在一级相变区深处，累积量趋近于预期的两相极限U_Q→2/3。采用多正则模拟，针对L≤24的系统直接由Wang–Landau态密度构造权重，对更大尺寸系统的权重进行重标度和精细化处理，直至L=64，得到界面张力指数μ=1.265(26)，与三临界预测值(d-1)/y_g=5/4一致。最后，利用相同的态密度数据绘制了相边界的连续分支，得到T_c(Δ=0)=1.157；足够接近三临界点的估计值受伊辛到三临界标度的交叉效应影响。
英文摘要
We present a high-resolution numerical study of the spin-1 Blume--Capel ferromagnet on the honeycomb lattice ($z=3$). Wang--Landau estimates of the joint density of states $Ω(E_1,E_2)$, combined with field mixing, are used to map the first-order transition line and locate the tricritical point at $(Δ_t,T_t)=[1.4819(2),\,0.4022(7)]$. Histogram reweighting of Metropolis simulations for $L=36$ and $48$ provides an independent consistency check, with a crossing temperature near $0.4039$, compatible with the Wang--Landau extrapolation. From the field-mixing analysis we obtain $r=-1.586(19)$, while the slope of the multicanonical coexistence line yields the consistent and more precise estimate $r=-1.587(5)$. Normalizing by the zero-temperature field $Δ_0=zJ/2$, the available honeycomb, square, triangular, and simple-cubic estimates cluster near $r/Δ_0\simeq-1.06$, corresponding to a magnitude about $6\%$ larger than the mean-field value $-1$; no systematic dependence on coordination number or dimensionality is resolved over the range examined. Finite-size scaling of $σ_Q$ gives $y_t=1.795(7)$, consistent with the tricritical Ising value $9/5$, while the fourth-order cumulant scaling is compatible with $y_g=4/5$. Deep in the first-order regime, the cumulant approaches the expected two-phase limit $U_Q\to2/3$. Multicanonical simulations up to $L=64$, using weights constructed directly from the Wang--Landau density of states for $L\le24$ and rescaled and refined for larger systems, yield an interface-tension exponent $μ=1.265(26)$, consistent with the tricritical prediction $(d-1)/y_g=5/4$. Finally, we map the continuous branch of the phase boundary from the same density-of-states data, obtaining $T_c(Δ=0)=1.157$; estimates sufficiently close to the tricritical point are affected by crossover from Ising to tricritical scaling.
