On the critical behavior of the Ising model with mixed two- and three-spin interactions

A study is made of a two-dimensional Ising model with staggered three-spin interactions in one direction and two-spin interactions in the other. The phase diagram of the model and its critical behavior are explored by conventional finite-size scaling and by exploiting relations between mass gap amplitudes and critical exponents predicted by conformal invariance. The model is found to exhibit a line of continuously varying critical exponents, which bifurcates into two Ising critical lines. This similarity of the model with the Ashkin-Teller model leads to a conjecture for the exact critical indices along the nonuniversal critical curve. Earlier contradictions about the universality class of the uniform (isotropic) case of the model are clarified.     

Multicritical behavior at the kosterlitz-thouless critical point

A multicritical critical point for the two dimensional planar model is analyzed by studying an exactly soluable limit of a related model—the generalized Villain model. The statistical mechanics of this model is written in terms of vortex and symmetry breaking excitations. In these terms, the problem reduces to a kind of two dimensional problem with interacting electric charges and magnetic monopoles. In this form, the problem is manifestly self-dual. The multicritical behavior is exhibited in a three-dimensional phase space in which the axes are the coupling strength of a “square” symmetry breaking which favors four possible directions for the planar model vectors. The analysis of this multicritical point shows that it is the intersection of at least six critical lines—each with continuously varying critical indices. Two of these lines are described by the exactly soluable gaussian model. The other four are isomorphic to one another, and each one has—as a point on the line—a critical point of the Ashkin-Teller model. We argue that each of these lines might be in an equivalent universality class to the line of critical points which occurs in the Baxter and Ashkin-Teller models. We make a suggestion about which point on these critical lines might be in the same universality class as our multicritical point. Correlation functions at the intersection point are calculated and used to develop an expansion of critical indices about this point. This expansion gives a potential method for calculating the critical behavior along the critical lines of the model.     

Critical Behavior of the Gaussian Model with Periodic Interactions on Diamond—Type Hierarchical Lattices in External Magnetic Fields

The Gaussian spin model with periodic interactions on the diamond-type hierarchical lattices is constructed by generalizing that with uniform interactions on translationally invariant lattices according to a class of substitution sequences.The Gaussian distribution constants and imposed external magnetic fields are also periodic depending on the periodic characteristic of the interaction onds.The critical behaviors of this generalized Gaussian model in external magnetic fields are studied by the exact renormalization-group approach and spin rescaling method.The critical points and all the critical exponents are obtained.The critical behaviors are found to be determined by the Gaussian distribution constants and the fractal dimensions of the lattices.When all the Gaussian distribution constants are the same,the dependence of the critical exponents on the dimensions of the lattices is the same as that of the Gaussian model with uniform interactions on translationally invariant lattices.     

Fractal Aggregation Near the Threshold

In this papel, we present two fractal aggregation models, line pattern seed model (model 1) and point pattern seed model (model 2), which are particle-cluster models. Using the current models, we investigate the critical transition in fractal aggregation processes in two dimensions, and suggest a method for finding the critical transition point. The computer simulation results show that the critical concentration is P_ca=0.69±0.02 for model 1 and P_ca=0.72±0.01 for model 2, critical fractal dimension. D_c= 1.71±0.06 for model 1 and D_c=1.66±0.07 for model 2, which are in good agreement with those of DLA model (D=5/3) and experimental data. The results also show that the critical transition point in two dimensions seems to be inilependent of the size of lattices and the initial seed patterns. The results seem to belong to the same universality class.     

Criticality of Epidemic Spreading in Mobile Individuals Mediated by Environment

We investigate the critical behaviour of an epidemical model in a diffusive population mediated by a static vector environment on a 2D network. It is found that this model presents a dynamical phase transition from disease-free state to endemic state with a finite population density. Finite-size and short-time dynamic scaling relations are used to determine the critical population density and the critical exponents characterizing the behaviour near the critical point. The results are compatible with the universality class of directed percolation coupled to a conserved diffusive field with equal diffusion constants.     

Random-bond Ising chain in a transverse magnetic field: A finite-size scaling analysis

We investigate the zero-temperature quantum phase transition of the randombond Ising chain in a transverse magnetic field. Its critical properties are identical to those of the McCoy-Wu model, which is a classical Ising model in two dimensions with layered disorder. The latter is studied via Monte Carlo simulations and transfer matrix calculations and the critical exponents are determined with a finite-size scaling analysis. The magnetization and susceptibility obey conventional rather than activated scaling. We observe that the order parameter and correlation function probability distribution show a nontrivial scaling near the critical point, which implies a hierarchy of critical exponents associated with the critical behavior of the generalized correlation lengths.     

Exact coexistence surfaces containing double critical points for a three-component solution on the Bethe,honeycomb, and square lattices

A model is considered in which the bonds of a lattice are covered by rodlike molecules. Neighboring molecular ends interact with orientation-dependent interactions. The model exhibits closed -loop phase diagrams and double critical points. Exact coexistence surfaces are calculated for the model on the Bethe, honeycomb, and square lattices. The nature of the doubling of the critical exponent near a double critical point is calculated. The behavior of the critical line in the neighborhood of a double critical point is calculated exactly.     

Critical area computation for real defects and arbitrary conductor shapes

In current critical area models, it is generally assumed the defect outlines are circular and the conductors to be rectangle or the merger of rectangles. However, real defects and conductors associated with optimal layout design exhibit a great variety of shapes. Based on mathematical morphology, a new critical area model is presented, which can be used to estimate the critical area of short circuit, open circuit and pinhole. Based on the new model, the efficient validity check algorithms are explored to extract critical areas of short circuit, open circuit and pinhole from layouts. The results of experiment on an approximate layout of ${4\times 4}$ shifts register show that the new model predicts the critical areas accurately. These results suggest that the proposed model and algorithm could provide new approaches for yield prediction.     

稍不均匀电场中低气压击穿的起始路径研究

稍不均匀电场间隙的起始击穿路径问题对于气体放电触发以及电极表面削蚀有重要意义.为研究低气压击穿工况中起始路径的位置规律,本文建立了一种基于蒙特卡罗碰撞模型与电子运动轨迹假设相结合的路径判断模型(determination of the critical path模型, DCP模型),并以2种电极装置的击穿试验来验证DCP模型的正确性.通过负电极表面的痕迹捕捉和击穿电压的测量可以分别验证DCP模型对起始击穿路径和击穿电压的计算能力.根据试验结果,起始击穿路径在不同压强或流率下会发生转移,且转移趋势与计算结果相符;同时, DCP模型对击穿电压的计算误差不超过7.9%,可初步验证DCP模型的计算精度.在此基础上,利用DCP模型对其他4种典型的电极装置进行数值计算,发现全部击穿案例都存在一些共性:随着间隙压强或流率的升高,最小电压区域((pd) min过渡区)的起始路径转移频繁,并伴随击穿电压上下波动,近似持平,且起始路径几乎都服从较长路径向较短路径的转移规律.最后,通过DCP模型的数值分析,揭示了上述起始路径相关规律的内在机理.     

Critical diffraction of irregular structure detonations and their predictability from experimentally obtained D−κ data

The present work reports new experiments of detonation diffraction in a 2D channel configuration in stoichiometric mixtures of ethylene, ethane, and methane with oxygen as oxidizer. The flow field details are obtained using high-speed schlieren near the critical conditions of diffraction. The critical initial pressure for successful diffraction is reported for the ethylene, ethane and methane mixtures. The flow field details revealed that the lateral portion of the wave results in a zone of quenched ignition. The dynamics of the laterally diffracting shock front are found in good agreement with the recent model developed by Radulescu et al. (Physics of Fluids 2021). The model provides noticeable improvement over the local models using Whitham’s characteristic rule and Wescott, Bdzil and Stewart’s model for weakly curved reactive shocks. These models provide a link between the critical channel height and the critical wave curvature. The critical channel heights and global curvatures are found in very good agreement with the critical curvatures measured independently by Xiao and Radulescu (Combust. Flame 2020) in quasi-steady experiments in exponential horns for three mixtures tested. Furthermore, critical curvature data obtained by others in the literature was found to provide a good prediction of critical diffraction in 2D. These findings suggest that the critical diffraction of unstable detonations may be well predicted by a model based on the maximum curvature of the detonation front, where the latter is to be measured experimentally and account for the role of the cellular structure in the burning mechanism. This finding provides support to the view that models for unstable detonations at a meso-scale larger than the cell size, i.e., hydrodynamic average models, are meaningful.     

Simulation of critical behaviour on damage evolution

Based on a damage evolution equation and a critical damage function model, this paper has completed the numerical simulation of ductile spall fracture. The free-surface velocity and damage distribution have been used to determine jointly the physical parameters D_l (the critical linking damage), D_f (the critical fracturing damage) and k (the softening rate of critical damage function model）of the critical damage function model, which are 0.11, 0.51 and 0.57 respectively. Results indicate that the parameters determined by any of shots could be applicable to the rest of other shots, which is convincing proof for the universal property of critical damage function. In our experiments, the shock pressure is about 1~GPa to 2.5~GPa. For the reason of limited pressure range, there are still some limitations in the methods of present analysis. Moreover, according to the damage evolution characteristic of pure aluminum obtained by experiments, two critical damages are obtained, which are 0.11 and 0.51 respectively. The results are coincident with the experimental ones, which indicate that the critical growth behaviour of damage occurs in the plastic metal under dynamic loading.     

Computer simulation of the critical behavior of 3D disordered ising model

The critical behavior of the disordered ferromagnetic Ising model is studied numerically by the Monte Carlo method in a wide range of variation of concentration of nonmagnetic impurity atoms. The temperature dependences of correlation length and magnetic susceptibility are determined for samples with various spin concentrations and various linear sizes. The finite-size scaling technique is used for obtaining scaling functions for these quantities, which exhibit a universal behavior in the critical region; the critical temperatures and static critical exponents are also determined using scaling corrections. On the basis of variation of the scaling functions and values of critical exponents upon a change in the concentration, the conclusion is drawn concerning the existence of two universal classes of the critical behavior of the diluted Ising model with different characteristics for weakly and strongly disordered systems.     

Size-asymmetric primitive model at low temperature: description of ion pairing and location of the critical point

We argue that Bjerrum's approach to ion pairing is inappropriate for the size-asymmetric primitive model in the neighborhood of its critical point, and propose a new approach based on the Stillinger-Lovett pairing procedure. The new approach recursively scales up the ion size until linear approximations are suitable for analyzing such a model. To locate the critical point, a residual van der Waals interaction between pairs is added, with an energy cutoff adjusted to match the critical temperature of the restricted primitive model. The locations and downward trends of T(c) and rho(c) with asymmetry are found to compare favorably with simulations.     

Self-Organization and Phase Transition in Two-Dimensional Traffic-Flow Model

An analytical investigation is made on two-dimensional traffic-flow model with alternative movement and exclude-volume effect between right and up arrows. Several exact results are obtained, including the upper critical density above which there are only jamming configurations, and the lower critical density below which there are only moving configurations. The observed jamming transition takes place at another critical density p_c(N), which is in the intermediate region between the lower and upper critical densities. This transition is suggested to be a second-order phase transition, the order parameter is found. The nature of self-organization, ergodicity breaking and synchronization are discussed. Comparison with the sandpile model is made.     

Phase transitions of bilayer spin-1/2 Baxter-Wu model with repulsive interlayer interactions

Using a Monte Carlo simulation and the single histogram reweighting technique, we study the critical behaviors and phase transitions of the Baxter-Wu model on a two-layer triangular lattice with repulsive interlayer interactions. Via the finite-size analysis, we obtain the transition temperatures and critical exponents at different interlayer coupling strengths. The reduced energy cumulants and the histograms reveal pseudo-first-order phase transitions, and the critical exponents derivate from the standard Baxter-Wu model if the coupling is weak. As the increase of the coupling, the behavior of the pseudo-first order transition disappears and the critical exponents are in accordance with the ones known for the 2D 4-state Potts model.     

特殊钻石型等级晶格上S4模型的临界性质

应用实空间重整化群和累积展开的方法，研究了外场中特殊钻石型等级晶格上S⁴模型的相变和临界性质，求出了系统的临界点和临界指数. 结果表明，此系统除了存在一个Gauss不动点外，还存在一个Wilson-Fisher不动点，与该等级晶格上的Gauss模型相比较，系统的临界指数发生了变化. 关键词： 钻石型等级晶格 4模型')" href="#">S⁴模型 重整化群 临界性质     

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.     

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.     

Dynamic critical behavior of the Heisenberg model with strong easy plane anisotropy

The dynamic critical behavior of the Heisenberg model with a strong anisotropy of the exchange constant in the z direction is investigated. The main features of the time evolution of this model are revealed. The static and dynamic critical behavior of planar magnetic models is shown to be described well by the Heisenberg model with strong easy plane anisotropy.