论文标题
Ising模型的关键指数$ν$在三个维度上具有蒙特卡洛技术分析的远距离相关站点障碍
Critical exponent $ν$ of the Ising model in three dimensions with long-range correlated site disorder analyzed with Monte Carlo techniques
论文作者
论文摘要
我们通过使用Monte Carlo模拟研究了Ising模型在具有现场障碍的晶格上的三个维度的临界行为。该疾病是不相关的或远程与相关函数相关的，该功能是根据power-law $ r^{ - a} $衰减的。我们通过将不同浓度的缺陷$ 0.05 \ leq p_d \ leq 0.4 $结合到一个全球拟合ANSATZ中，并应用有限大小的缩放技术，从而得出了相关长度$ν$的关键指数和汇合校正指数$ω$的依赖性$ a $。我们模拟和研究各种不同的相关指数$ 1.5 \ leq a \ leq 3.5 $以及不相关的案例$ a = \ infty $，并且能够提供以前的作品尚不知道的全球图片。此外，我们对远程相关性疾病的组合进行了专门的分析，并为系统的临界温度估算了相关指数$ a $ a $和缺陷的浓度$ p_d $。我们将我们的结果与其他作品的已知结果以及Weinrib和Halperin的猜想进行了比较：$ν= 2/a $，并讨论发生的偏差。
We study the critical behavior of the Ising model in three dimensions on a lattice with site disorder by using Monte Carlo simulations. The disorder is either uncorrelated or long-range correlated with correlation function that decays according to a power-law $r^{-a}$. We derive the critical exponent of the correlation length $ν$ and the confluent correction exponent $ω$ in dependence of $a$ by combining different concentrations of defects $0.05 \leq p_d \leq 0.4$ into one global fit ansatz and applying finite-size scaling techniques. We simulate and study a wide range of different correlation exponents $1.5 \leq a \leq 3.5$ as well as the uncorrelated case $a = \infty$ and are able to provide a global picture not yet known from previous works. Additionally, we perform a dedicated analysis of our long-range correlated disorder ensembles and provide estimates for the critical temperatures of the system in dependence of the correlation exponent $a$ and the concentrations of defects $p_d$. We compare our results to known results from other works and to the conjecture of Weinrib and Halperin: $ν= 2/a$ and discuss the occurring deviations.
