Speck Thomas
Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany.
Phys Rev E. 2022 Jun;105(6-1):064601. doi: 10.1103/PhysRevE.105.064601.
We explore the relation between active Brownian particles, a minimal particle-based model for active matter, and scalar field theories. Both show a liquid-gas-like phase transition toward stable coexistence of a dense liquid with a dilute active gas that terminates in a critical point. However, a comprehensive mapping between the particle-based model parameters and the effective coefficients governing the field theories has not been established yet. We discuss conflicting recent numerical results for the critical exponents of active Brownian particles in two dimensions. Starting from the intermediate effective hydrodynamic equations, we then present a construction for a scalar order parameter for active Brownian particles that yields the active model B+. We argue that a crucial ingredient is the coupling between density and polarization in the particle current. The renormalization flow close to two dimensions exhibits a pair of perturbative fixed points that limit the attractive basin of the Wilson-Fisher fixed point, with the perspective that the critical behavior of active Brownian particles in two dimensions is governed by a strong-coupling fixed point different from Wilson-Fisher and not necessarily corresponding to Ising universality.
我们探究了活性布朗粒子（一种用于活性物质的基于粒子的最小模型）与标量场理论之间的关系。两者都呈现出类似液 - 气的相变，即朝着致密液体与稀薄活性气体稳定共存的方向转变，并在临界点处终止。然而，基于粒子的模型参数与控制场理论的有效系数之间尚未建立全面的映射关系。我们讨论了近期关于二维活性布朗粒子临界指数的相互矛盾的数值结果。从中间有效的流体动力学方程出发，我们给出了一种用于活性布朗粒子的标量序参量的构建方法，该方法得到了活性模型B +。我们认为一个关键因素是粒子流中密度与极化之间的耦合。接近二维的重整化流展现出一对微扰不动点，这些不动点限制了威尔逊 - 费舍尔不动点的吸引域，由此认为二维活性布朗粒子的临界行为由一个不同于威尔逊 - 费舍尔且不一定对应伊辛普适性的强耦合不动点所支配。
