Phase transitions in a non-perturbative regime can be studied by ab initio Lattice Field Theory methods. The status and future research directions for LFT investigations of Quantum Chromo-Dynamics under extreme conditions are reviewed, including properties of hadrons and of the hypothesized QCD axion as inferred from QCD topology in different phases. We discuss phase transitions in strong interactions in an extended parameter space, and the possibility of model building for Dark Matter and Electro-Weak Symmetry Breaking. Methodological challenges are addressed as well, including new developments in Artificial Intelligence geared towards the identification of different phases and transitions.

非微扰状态下的相变可以通过从头开始晶格场论方法来研究。综述了极端条件下量子色动力学 LFT 研究的现状和未来研究方向，包括强子的性质和从不同相的QCD 拓扑推断的假设的 QCD 轴子的性质。我们讨论了扩展参数空间中强相互作用中的相变，以及暗物质和电弱对称性破缺模型构建的可能性。方法论挑战也得到解决，包括人工智能的新发展，旨在识别不同的阶段和转变。