发表机构
University of Wuppertal; Forschungszentrum Jülich（伍珀塔尔大学; 于利希研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究三维$\phi^4$理论的临界耦合，通过晶格模拟和连续极限外推，确定了临界参数$f_\mathrm{c}=18.808(78)$及$\Delta\langle\phi^2\rangle_\mathrm{c}/\lambda=-0.00303(17)$。
AI 中文摘要
我们考虑在三维欧几里得空间中$\phi(x)\in\mathbb{R}$的$\phi^4$理论。对于多种自耦合$\hat{\lambda}$，确定了临界（裸）参数$\hat{\mu}_{0\mathrm{c}}^2(\hat{\lambda})$，此时晶格正则化系统从对称相转变到破缺相。接下来，我们将盒体积推向无穷大并切换到普适方案；这为每个模拟的$\hat{\lambda}$给出了$\hat{\mu}_\mathrm{c}^2(\hat{\lambda})$。最后，连续极限外推给出$f_\mathrm{c}=\lim_{\hat{\lambda}\to0} \hat{\lambda}^2/\hat{\mu}_\mathrm{c}^2(\hat{\lambda})$，我们发现$f_\mathrm{c} = 18.808(64)_{\mathrm{stat}}(45)_{\mathrm{sys}} = 18.808(78)_{\mathrm{tot}}$。此外，在连续极限和无穷体积极限的联合极限下确定了$\Delta\langle\phi^2\rangle_\mathrm{c}/\lambda = -0.00303(12)_{\mathrm{stat}}(12)_{\mathrm{sys}} = -0.00303(17)_{\mathrm{tot}}$。
英文摘要
We consider the $ϕ^4$ theory with $ϕ(x)\in\mathbb{R}$ in three Euclidean dimensions. For a variety of self-couplings $\hatλ$, the critical (bare) parameter $\hatμ_{0\mathrm{c}}^2(\hatλ)$ is determined where the lattice-regulated system changes from the symmetric phase to the broken phase. Next, we send the box volume to infinity and switch to a universal scheme; this yields $\hatμ_\mathrm{c}^2(\hatλ)$ for each simulated $\hatλ$. Finally, a continuum extrapolation gives $f_\mathrm{c}=\lim_{\hatλ\to0} \hatλ^2/\hatμ_\mathrm{c}^2(\hatλ)$, and we find $f_\mathrm{c} = 18.808(64)_{\mathrm{stat}}(45)_{\mathrm{sys}} = 18.808(78)_{\mathrm{tot}}$. In addition, $Δ\langleϕ^2\rangle_\mathrm{c}/λ= -0.00303(12)_{\mathrm{stat}}(12)_{\mathrm{sys}} = -0.00303(17)_{\mathrm{tot}}$ is determined in the combined continuum and infinite-volume limit.
Comments22 pages, 11 figures, 14 tables
