Akın Kutay, Berker A Nihat
Department of Electrical and Electronics Engineering, Boğaziçi University, Bebek, Istanbul 34342, Turkey.
Department of Physics, Boğaziçi University, Bebek, Istanbul 34342, Turkey.
Phys Rev E. 2022 Jul;106(1-1):014151. doi: 10.1103/PhysRevE.106.014151.
The random-field XY model is studied in spatial dimensions d=3 and 4, and in between, as the limit q→∞ of the q-state clock models, by the exact renormalization-group solution of the hierarchical lattice or, equivalently, the Migdal-Kadanoff approximation to the hypercubic lattices. The lower critical dimension is determined between 3.81<d_{c}<4. When the random field is scaled with q, a line segment of zero-temperature criticality is found in d=3. When the random field is scaled with q^{2}, a universal phase diagram is found at intermediate temperatures in d=3.
通过分层晶格的精确重整化群解，或者等效地，通过超立方晶格的Migdal-Kadanoff近似，研究了空间维度d = 3和4以及介于两者之间作为q态时钟模型q→∞极限的随机场XY模型。确定了下临界维度在3.81 < d_c < 4之间。当随机场按q缩放时，在d = 3中发现了零温度临界性的线段。当随机场按q²缩放时，在d = 3的中间温度下发现了一个通用相图。
