Extensive numerical simulations on competitive growth between the Edwards–Wilkinson and Kardar–Parisi–Zhang universality classes

Extensive numerical simulations and scaling analysis are performed to investigate competitive growth between the linear and nonlinear stochastic dynamic growth systems, which belong to the Edwards–Wilkinson(EW) and Kardar–Parisi–Zhang(KPZ) universality classes, respectively. The linear growth systems include the EW equation and the model of random deposition with surface relaxation(RDSR), the nonlinear growth systems involve the KPZ equation and typical discrete models including ballistic deposition(BD), etching, and restricted solid on solid(RSOS). The scaling exponents are obtained in both the(1 + 1)-and(2 + 1)-dimensional competitive growth with the nonlinear growth probability p and the linear proportion 1-p. Our results show that, when p changes from 0 to 1, there exist non-trivial crossover effects from EW to KPZ universality classes based on different competitive growth rules. Furthermore, the growth rate and the porosity are also estimated within various linear and nonlinear growths of cooperation and competition.

Universality Class in Abelian Sandpile Models with Stochastic Toppling Rules

We present a stochastic critical slope sandpile model, where the amount of grains that fall in an overturning event is stochastic variable. The model is local, conservative, and Abelian. We apply the moment analysis to evaluate critical exponents and finite size scaling method to consistently test the obtained results. Numerical results show that this model, Oslo model, and one-dimensional Abelian Manna model have the same critical behavior although the three models have different stochastic toppling rules, which provides evidences suggesting that Abelian sandpile models with different stochastic toppling rules are in the same universality class.

Application of Dijkstra Algorithm to Proposed Tramway of a Potential World Class University

Nowadays, the development of “smart cities” with a high level of quality of life is becoming a prior challenge to be addressed. In this paper, promoting the model shift in railway transportation using tram network towards more reliable, greener and in general more sustainable transportation modes in a potential world class university is proposed. “Smart mobility” in a smart city will significantly contribute to achieving the goal of a university becoming a world class university. In order to have a regular and reliable rail system on campus, we optimize the route among major stations on campus, using shortest path problem Dijkstra algorithm in conjunction with a computer software called LINDO to arrive at the optimal route. In particular, it is observed that the shortest path from the main entrance gate (Canaan land entrance gate) to the Electrical Engineering Department is of distance 0.805 km.

Lessons in Love——University class attracts huge crowds of curious onlookers

Zhou Dan, an articulate lawyer, led a semi-secret life until recently when he was invited to give a talk to the Homosexual Studies class at Fudan University in Shanghai.

A Solvable Decorated Ising Lattice Model

A decorated lattice is suggested and the Ising model on it with three kinds of interactions K1, K2, and K3 is studied. Using an equivalent transformation, the square decorated Ising lattice is transformed into a regular square Ising lattice with nearest-neighbor, next-nearest-nelghbor, and four-spin interactions, and the critical fixed point is found at K1 = 0.5769, K2= -0.0671, and K3 = 0.3428, which determines the critical temperature of the system. It is also found that this system and the regular square Ising lattice, and the eight-vertex model belong to the same universality class.

Critical Behaviors in a Stochastic Local Limited One-Dimensional Rice-Pile Model

A stochastic local limited one-dimensional rice-pile model is numerically investigated. The distributions for avalanche sizes have a clear power-law behavior and it displays a simple finite size scaling. We obtain the avalanche exponents Ts= 1.54±0.10,βs = 2.17±0.10 and TT = 1.80±0.10, βT =1.46 ± 0.10. This self-organized critical model belongs to the same universality class with the Oslo rice-pile model studied by K. Christensen et al. [Phys. Rev. Lett. 77 （1996） 107], a rice-pile model studied by L.A.N. Amaral et al. [Phys. Rev. E 54 （1996） 4512], and a simple deterministic self-organized critical model studied by M.S. Vieira [Phys. Rev. E 61 （2000） 6056].

Critical Behaviors in a Stochastic One-Dimensional Sand-Pile Model

A one-dimensional sand-pile model (Manna model), which has a stochastic redistribution process, is studied both in discrete and continuous manners. The system evolves into a critical state after a transient period. A detailed analysis of the probability distribution of the avalanche size and duration is numerically investigated. Interestingly,contrary to the deterministic one-dimensional sand-pile model, where multifractal analysis works well, the analysis based on simple finite-size scaling is suited to fitting the data on the distribution of the avalanche size and duration. The exponents characterizing these probability distributions are measured. Scaling relations of these scaling exponents and their universality class are discussed.

Quantum Monte Carlo study on the phase transition for a generalized two-dimensional staggered dimerized Heisenberg model

In order to gain a deeper understanding of the quantum criticality in the explicitly staggered dimerized Heisenberg models, we study a generalized staggered dimer model named the J0 J1 J2 model, which corresponds to the staggered j-j′ model on a square lattice and a honeycomb lattice when J1/J0 equals 1 and O, respectively. Using the quantum Monte Carlo method, we investigate all the quantum critical points of these models with J1/J0 changing from 0 to 1 as a function of coupling ratio a = J2/J0. We extract all the critical values of the coupling ratio ac for these models, and we also obtain the critical exponents v,β/ν, and η using different finite-size scaling ansatz,. All these exponents are not consistent with the three-dimensional Heisenberg universality class, indicating some unconventional quantum ciriteial points in these models.

Machine learning phase transitions of the three-dimensional Ising universality class

Exploration of the QCD phase diagram and critical point is one of the main goals in current relativistic heavy-ion collisions.The QCD critical point is expected to belong to a three-dimensional(3D)Ising universality class.Machine learning techniques are found to be powerful in distinguishing different phases of matter and provide a new way to study the phase diagram.We investigate phase transitions in the 3D cubic Ising model using supervised learning methods.It is found that a 3D convolutional neural network can be trained to effectively predict physical quantities in different spin configurations.With a uniform neural network architecture,it can encode phases of matter and identify both second-and first-order phase transitions.The important features that discriminate different phases in the classification processes are investigated.These findings can help study and understand QCD phase transitions in relativistic heavy-ion collisions.

Universality class of machine learning for critical phenomena

Herein,percolation phase transitions on a two-dimensional lattice were studied using machine learning techniques.Results reveal that different phase transitions belonging to the same universality class can be identified using the same neural networks(NNs),whereas phase transitions of different universality classes require different NNs.Based on this finding,we proposed the universality class of machine learning for critical phenomena.Furthermore,we investigated and discussed the NNs of different universality classes.Our research contributes to machine learning by relating the NNs with the universality class.

Fixed point behavior of cumulants in the three-dimensional Ising universality class

High-order cumulants and factorial cumulants of conserved charges are suggested for the study of the critical dynamics in heavy-ion collision experiments. In this paper, using the parametric representation of the threedimensional Ising model which is believed to belong to the same universality class as quantum chromo-dynamics,the temperature dependence of the second-to fourth-order(factorial) cumulants of the order parameter is studied. It is found that the values of the normalized cumulants are independent of the external magnetic field at the critical temperature, which results in a fixed point in the temperature dependence of the normalized cumulants. In finite-size systems simulated using the Monte Carlo method, this fixed point behavior still exists at temperatures near the critical. This fixed point behavior has also appeared in the temperature dependence of normalized factorial cumulants from at least the fourth order. With a mapping from the Ising model to QCD, the fixed point behavior is also found in the energy dependence of the normalized cumulants(or fourth-order factorial cumulants) along different freezeout curves.

Observation of thickness-tuned universality class in superconducting β-W thin films

The interplay between quenched disorder and critical behavior in quantum phase transitions is conceptually fascinating and of fundamental importance for understanding phase transitions. However, it is still unclear whether or not the quenched disorder influences the universality class of quantum phase transitions. More crucially, the absence of superconducting-metal transitions under in-plane magnetic fields in 2D superconductors imposes constraints on the universality of quantum criticality. Here, we observe the thickness-tuned universality class of superconductor-metal transition by changing the disorder strength in b - W films with varying thickness. The finite-size scaling uncovers the switch of universality class: quantum Griffiths singularity to multiple quantum criticality at a critical thickness of tc⊥1~ 8 nm and then from multiple quantum criticality to single criticality at tc⊥2~ 16 nm. Moreover, the superconducting-metal transition is observed for the first time under in-plane magnetic fields and the universality class is changed at tc‖~ 8 nm. The observation of thickness-tuned universality class under both out-of-plane and in-plane magnetic fields provides broad information for the disorder effect on superconducting-metal transitions and quantum criticality.

Cumulants in the 3-dimensional Ising, O(2) and O(4) spin models

Based on the universal properties of a critical point in different systems and that the QCD phase transitions fall into the same universality classes as the 3-dimensional Ising, O（2） or O（4） spin models, the critical behavior of cumulants and higher cumulant ratios of the order parameter from the three kinds of spin models is studied. We found that all higher cumulant ratios change dramatically the sign near the critical temperature. The qualitative critical behavior of the same order cumulant ratio is consistent in these three models.

Free energy fluctuations for a mixture of directed polymers

We study the free energy fluctuations for a mixture of directed polymers, which was first introduced by Borodin et al. （2015） to investigate the limiting distribution of a stationary Kaxdar-Parisi-Zhang （KPZ） equation. The main results consist of both the law of large numbers and the asymptotic fluctuation for the free energy as the model size tends to infinity. In particular, we find the explicit values （which may depend on model parameters） of normalizing constants in the fluctuation. This shows that such a mixture model is in the KPZ university class.

Scaling relation of domain competition on(2+1)-dimensional ballistic deposition model with surface diffusion

During heteroepitaxial overlayer growth multiple crystal domains nucleated on a substrate surface compete with each other in such a manner that a domain covered by neighboring ones stops growing.The number density of active domains ρ decreases as the height h increases.A simple scaling argument leads to a scaling law of ρ~ h^（-γ） with a coarsening exponent γ=d/z,where d is the dimension of the substrate surface and z the dynamic exponent of a growth front.This scaling relation is confirmed by performing kinetic Monte Carlo simulations of the ballistic deposition model on a two-dimensional（d=2） surface,even when an isolated deposited particle diffuses on a crystal surface.