三维Z(2)和O(2)自旋模型在非零对称破缺参数下的有限尺寸标度分析
Finite-size scaling analysis of three dimensional Z(2) and O(2) spin models with non-vanishing symmetry breaking parameter
- Universität Bielefeld（比勒费尔德大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
通过高统计量蒙特卡洛数据，对三维Z(2)和O(2)自旋模型进行有限尺寸标度分析，获得前导修正并建立参数化形式，消除QCD手征相变温度分析中的系统误差，并指出两普适类的差异。
AI中文摘要：
我们展示了在外场H中三维Z(2)和O(2)自旋模型的详细有限尺寸标度分析结果。利用高统计量蒙特卡洛数据，我们获得了对无穷体积标度函数的前导有限尺寸标度修正。我们证明这些修正与\widetilde{z}_L^2=1/(H L^{3/(1+1/\delta))})^{2}成正比。这为体热力学观测量以及非零H下确定的赝临界温度提供了有限尺寸修正的参数化形式。特别是，它允许消除在(2+1)味QCD手征相变温度分析中由于先前未良好控制的无穷体积外推假设而产生的系统误差。我们还建立了该前导修正的有效范围，并指出三维O(2)和Z(2)普适类之间存在显著差异。
英文摘要：
We present results from a detailed finite-size scaling analysis of the $3$-$d$, $Z(2)$ and $O(2)$ spin models in an external field $H$. Using high statistics Monte Carlo data, we obtain the leading finite-size scaling correction to the infinite volume scaling functions. We show that these corrections are proportional to $\widetilde{z}_L^2=1/(H L^{3/(1+1/δ))})^{2}$. This provides the parametric form for finite-size corrections to bulk thermodynamic observables as well as the pseudo-critical temperatures determined at non-vanishing $H$. In particular, it allows to eliminate systematic errors in the analysis of the chiral phase transition temperature in (2+1)-flavor QCD, that arose from the previously not well-controlled ansatz for infinite volume extrapolations. We also establish the validity range of this leading order correction and point out that there are significant differences between the $3$-$d$, $O(2)$ and $Z(2)$ universality classes.
