模糊洋葱上标量场理论的数值研究
Numerical Study of Scalar Field Theory on the Fuzzy Onion
浏览论文内容
中文总结 AI 辅助
本研究针对三维矩阵模型模糊洋葱上的标量场理论，用哈密顿蒙特卡洛模拟研究其相结构，确定了均匀相边界等两个相变边界，并与模糊球面相结构对比。
中文摘要 AI 辅助
我们研究模糊洋葱模型上标量场理论的行为，该模型是一种三维矩阵模型，由半径逐渐增大的同心模糊球面构成。我们采用哈密顿蒙特卡洛模拟这一数值方法研究该理论的相结构，识别出场的各个相，探究并描述动力学相变现象，尝试重构相变线。我们将结果与已被充分研究的模糊球面相结构进行比较，最终确定该理论相变的两个边界：均匀相边界，以及无序相与非均匀相之间的临界边界。
英文摘要
We study the behaviour of the scalar field theory on the fuzzy onion model -- a three-dimensional matrix model consisting of concentric fuzzy spheres of gradually increasing radii. We use a numerical method of Hamiltonian Monte Carlo simulations to study the phase structure of this theory. We identify the field phases, investigate and describe a phenomenon of dynamical phase transitions and attempt to reconstruct phase transition lines. We compare the results with the well-studied phase structure of the fuzzy sphere. Finally, we identify two boundaries on the phase transitions of the theory, a uniform phase boundary and a critical boundary between the disordered and non-uniform phase.
