论文标题
与远程时间相互作用的关键现象理论
Theory of Critical Phenomena with Long-Range Temporal Interaction
论文作者
论文摘要
我们为关键现象开发了一个系统的理论，并在所有空间维度中具有内存，包括$ d <d_c $，$ d = d_c $和$ d> d_c $，上限临界维度。我们表明，汉密尔顿人在动力学中起着独特的作用，并且体现了时空和时间之间亲密关系的尺寸常数$ \ mathfrak {d} _t $是理论的基本成分。但是，它的值随空间维度的连续变化而变化，并在$ d = 4 $时完全消失，这反映了传递到空间尺寸的时间尺寸的变化，并以波动的强度转移到空间上。时间维度的这种变化节省了所有扩展定律，尽管违反了波动散文定理。出现了各种新的普遍性课程。
We develop a systematic theory for the critical phenomena with memory in all spatial dimensions, including $d<d_c$, $d=d_c$, and $d>d_c$, the upper critical dimension. We show that the Hamiltonian plays a unique role in dynamics and the dimensional constant $\mathfrak{d}_t$ that embodies the intimate relationship between space and time is the fundamental ingredient of the theory. However, its value varies with the space dimension continuously and vanishes exactly at $d=4$, reflecting reasonably the variation of the amount of the temporal dimension that is transferred to the spatial one with the strength of fluctuations. Such variations of the temporal dimension save all scaling laws though the fluctuation-dissipation theorem is violated. Various new universality classes emerge.
