Woo Chul-Ung, Noh Jae Dong
Department of Physics, University of Seoul, Seoul 02504, Korea.
Phys Rev E. 2024 Jan;109(1-1):014105. doi: 10.1103/PhysRevE.109.014105.
We introduce a Brownian p-state clock model in two dimensions and investigate the nature of phase transitions numerically. As a nonequilibrium extension of the equilibrium lattice model, the Brownian p-state clock model allows spins to diffuse randomly in the two-dimensional space of area L^{2} under periodic boundary conditions. We find three distinct phases for p>4: a disordered paramagnetic phase, a quasi-long-range-ordered critical phase, and an ordered ferromagnetic phase. In the intermediate critical phase, the magnetization order parameter follows a power-law scaling m∼L^{-β[over ̃]}, where the finite-size scaling exponent β[over ̃] varies continuously. These critical behaviors are reminiscent of the double Berezinskii-Kosterlitz-Thouless (BKT) transition picture of the equilibrium system. At the transition to the disordered phase, the exponent takes the universal value β[over ̃]=1/8, which coincides with that of the equilibrium system. This result indicates that the BKT transition driven by the unbinding of topological excitations is robust against the particle diffusion. On the contrary, the exponent at the symmetry-breaking transition to the ordered phase deviates from the universal value β[over ̃]=2/p^{2} of the equilibrium system. The deviation is attributed to a nonequilibrium effect from the particle diffusion.
我们引入了一个二维布朗p态时钟模型，并对相变的性质进行了数值研究。作为平衡晶格模型的非平衡扩展，布朗p态时钟模型允许自旋在面积为(L^{2})的二维空间中在周期性边界条件下随机扩散。对于(p>4)，我们发现了三个不同的相：无序顺磁相、准长程序临界相和有序铁磁相。在中间临界相中，磁化序参量遵循幂律标度(m∼L^{-\widetilde{\beta}})，其中有限尺寸标度指数(\widetilde{\beta})连续变化。这些临界行为让人联想到平衡系统的双重贝雷津斯基-科斯特利茨- Thouless（BKT）转变图像。在向无序相转变时，指数取通用值(\widetilde{\beta}=1/8)，这与平衡系统的指数一致。这一结果表明，由拓扑激发的解束缚驱动的BKT转变对粒子扩散具有鲁棒性。相反，向有序相的对称破缺转变时的指数偏离了平衡系统的通用值(\widetilde{\beta}=2/p^{2})。这种偏差归因于粒子扩散的非平衡效应。
