标题： 无序晶格玻璃 $φ^{4}$ 量子场论 显示英文标题

标题： Disordered Lattice Glass $φ^{4}$ Quantum Field Theory

摘要： 我们数值研究了三维$\phi^{4}$自旋玻璃，这是一种典型的无序且离散化的欧几里得场理论，它在空间和时间上表现出不均匀性，但考虑了均匀的平方质量项和lambda项。 $\phi^{4}$晶格玻璃场理论是对自旋玻璃的概念性推广，适用于连续自由度，我们讨论了一个极限的存在，在该极限下它形式上可简化为爱德华-安德森模型。 通过定义四种适用于连续自旋玻璃的序参量变体，我们数值验证了在没有磁化的情况下重叠的出现，从而确认了临界平方质量值下自旋玻璃相变的存在。 最后，我们讨论了如何利用$\phi^{4}$自旋玻璃来检验空间或时间的完全均匀性假设，并且如何在统计物理的并行框架下，从无序晶格和构造场论的角度，提供一个适合研究机器学习算法非微扰动力学的框架。 显示英文摘要

摘要： We study numerically the three-dimensional $\phi^{4}$ spin glass, a prototypical disordered and discretized Euclidean field theory that manifests inhomogeneities in space and time but considers a homogeneous squared mass and lambda terms. The $\phi^{4}$ lattice glass field theory is a conceptual generalization of spin glasses to continuous degrees of freedom and we discuss the existence of a limit under which it formally reduces to the Edwards-Anderson model. By defining four variants of an order parameter which are suitable for continuous spin glasses, we verify numerically the emergence of an overlap in absence of the magnetization thus confirming the presence of a spin glass phase transition for a value of a critical squared mass. We conclude by discussing how the $\phi^{4}$ spin glass can be utilized to address assumptions of complete homogeneity in space or time and how, in parallel to statistical physics, provides a suitable framework to investigate the nonperturbative dynamics of machine learning algorithms from the perspective of disordered lattice and constructive field theory.