Dynamic vortex Mott transition in triangular superconducting arrays

The proximity-coupled superconducting island arrays on a metallic film provide an ideal platform to study the phase transition of vortex states under mutual interactions between the vortex and potential landscape. We have developed a top-down microfabrication process for Nb island arrays on Au film by employing an Al hard mask. A current-induced dynamic vortex Mott transition has been observed under the perpendicular magnetic fields of $f$ magnetic flux quantum per unit cell, which is characterized by a dip-to-peak reversal in differential resistance $dV/dI$ vs. $f$ curve with the increasing current. The $dV/dI$ vs. $I$ characteristics show a scaling behavior near the magnetic fields of $f=\frac{1}{2}$ and $f=1$, with the critical exponents $\varepsilon$ of 0.45 and 0.3 respectively, suggesting different universality classes at these two fields.

Connecting Complex Electronic Pattern Formation to Critical Exponents

Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it pertains to those geometric clusters (defined as connected sets of nearest-neighbor aligned spins) in the context of Ising models. We show how data from surface probes can be used to distinguish whether electronic patterns observed at the surface of a material are confined to the surface, or whether the patterns originate in the bulk. Whereas thermodynamic critical exponents are derived from the behavior of Fortuin–Kasteleyn (FK) clusters, critical exponents can be similarly defined for geometric clusters. We find that these geometric critical exponents are not only distinct numerically from the thermodynamic and uncorrelated percolation exponents, but that they separately satisfy scaling relations at the critical fixed points discussed in the text. We furthermore find that the two-dimensional (2D) cross-sections of geometric clusters in the three-dimensional (3D) Ising model display critical scaling behavior at the bulk phase transition temperature. In particular, we show that when considered on a 2D slice of a 3D system, the pair connectivity function familiar from percolation theory displays more robust critical behavior than the spin-spin correlation function, and we calculate the corresponding critical exponent. We discuss the implications of these two distinct length scales in Ising models. We also calculate the pair connectivity exponent in the clean 2D case. These results extend the theory of geometric criticality in the clean Ising universality classes, and facilitate the broad application of geometric cluster analysis techniques to maximize the information that can be extracted from scanning image probe data in condensed matter systems.

Multiple magnetic phase transitions with different universality classes in bilayer La$$_{1.4}$$Sr$$_{1.6}$$Mn$$_{2}$$O$$_7$$ manganite

Here, we report three magnetic transitions at 101 K (T$$_{C1}$$ C 1 ), 246 K (T$$_{C2}$$ C 2 ) and 295 K (T$$_{C3}$$ C 3 ) in bilayer La$$_{1.4}$$ 1.4 Sr$$_{1.6}$$ 1.6 Mn$$_{2}$$ 2 O$$_7$$ 7 . The second order phase transitions have been identified at these transition points with the help of change in entropy analysis and modified Arrott plots (MAPs). The critical behavior around T$$_{C1}$$ C 1 , T$$_{C2}$$ C 2 and T$$_{C3}$$ C 3 have been studied by MAPs and Kouvel–Fisher method. Based on these analyses four magnetic phases are: (1) 2D Ising ferromagnetic (FM) below T$$_{C1}$$ C 1 ,(2) 2D Heisenberg canted antiferromagnetic (CAFM-I) and FM clusters in temperature range T$$_{C1}$$ C 1 < T < T$$_{C2}$$ C 2 , (3) 2D Heisenberg CAFM-II and FM clusters with non magnetically interacting planes in temperature range T$$_{C2}$$ C 2 < T < T$$_{C3}$$ C 3 and (4) paramagnetic for T > T$$_{C3}$$ C 3 .

Emergence of universality in the transmission dynamics of COVID-19

The complexities involved in modelling the transmission dynamics of COVID-19 has been a roadblock in achieving predictability in the spread and containment of the disease. In addition to understanding the modes of transmission, the effectiveness of the mitigation methods also needs to be built into any effective model for making such predictions. We show that such complexities can be circumvented by appealing to scaling principles which lead to the emergence of universality in the transmission dynamics of the disease. The ensuing data collapse renders the transmission dynamics largely independent of geopolitical variations, the effectiveness of various mitigation strategies, population demographics, etc. We propose a simple two-parameter model—the Blue Sky model—and show that one class of transmission dynamics can be explained by a solution that lives at the edge of a blue sky bifurcation. In addition, the data collapse leads to an enhanced degree of predictability in the disease spread for several geographical scales which can also be realized in a model-independent manner as we show using a deep neural network. The methodology adopted in this work can potentially be applied to the transmission of other infectious diseases and new universality classes may be found. The predictability in transmission dynamics and the simplicity of our methodology can help in building policies for exit strategies and mitigation methods during a pandemic.

Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws

We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ‘+’ or ‘−’, ‘up’ or ‘down’, ‘yes’ or ‘no’), differ in their strength. To investigate the interplay between variable properties of nodes and interactions between them, we study the model on a complex network where both the spin strength and degree distributions are governed by power laws. We show that in the annealed network approximation, thermodynamic functions of the model are self-averaging and we obtain an exact solution for the partition function. This allows us derive the leading temperature and field dependencies of thermodynamic functions, their critical behavior, and logarithmic corrections at the interface of different phases. We find the delicate interplay of the two power laws leads to new universality classes.