二维分级库仑气体的重整化群流
Renormalization Group Flow of the Two-Dimensional Hierarchical Coulomb Gas
摘要：
本文考虑二维分层库仑系统的重整化群变换所对应的拟线性抛物型微分方程，当块L为1时，得到了该方程在极限下的解。我们表明，初值问题是定义在一个合适的函数空间和解决方案收敛，当t趋于无穷大，可数无穷平衡解之一。非平凡的平衡解从平凡的平衡解分叉出来。这些解决方案进行了充分的描述，我们提供了一个完整的分析，其本地和全球的稳定性的所有值的逆温度。本文还讨论了Gallavotti和Nicolo关于"相变“无穷序列的猜想。我们的研究结果排除了中间阶段之间的血浆和Kosterlitz无菌阶段，至少在分层模型，我们认为。
英文摘要：
We consider a quasilinear parabolic differential equation associated with the renormalization group transformation of the two-dimensional hierarchical Coulomb system in the limit as the size of the block L goes to 1. We show that the initial value problem is well defined in a suitable function space and the solution converges, as t goes to infinity, to one of the countably infinite equilibrium solutions. The nontrivial equilibrium solution bifurcates from the trivial one. These solutions are fully described and we provide a complete analysis of their local and global stability for all values of inverse temperature. Gallavotti and Nicolo's conjecture on infinite sequence of ``phases transitions'' is also addressed. Our results rule out an intermediate phase between the plasma and the Kosterlitz-Thouless phases, at least in the hierarchical model we consider.
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