Spontaneous-search method and short-time dynamics: applications to the Domany-Kinzel cellular automaton

The one-dimensional Domany-Kinzel cellular automaton is investigated by two numerical approaches: (i) the spontaneous-search method, which is a method appropriated for a search of criticality; (ii) short-time dynamics. Both critical frontiers of the system are investigated, namely, the one separating the frozen and active phases, as well as the critical line determined by damage spreading between two cellular automata, that splits the active phase into the nonchaotic and chaotic phases. The efficiency of the spontaneous-search method is established herein through a precise estimate of both critical frontiers, and in addition to that, it is shown that this method may also be used in the determination of the critical exponent ν_⊥. Using the critical frontiers obtained, other exponents are estimated through short-time dynamics. It is verified that the critical exponents of both critical frontiers fall in the universality class of directed percolation.     

Detecting topological order through a continuous quantum phase transition

We study a continuous quantum phase transition that breaks a Z2 symmetry. We show that the transition is described by a new critical point which does not belong to the Ising universality class, despite the presence of well-defined symmetry-breaking order parameter. The new critical point arises since the transition not only breaks the Z2 symmetry, it also changes the topological or quantum order in the two phases across the transition. We show that the new critical point can be identified in experiments by measuring critical exponents. So measuring critical exponents and identifying new critical points is a way to detect new topological phases and a way to measure topological or quantum orders in those phases.     

Renormalization of the 1/N expansion and critical behaviour of (2+1)-dimensional supersymmetric non-linear sigma-models

Renormalized 1/N expansion in both high-and low-temperature phases as well as of the critical theory of three-dimensional supersymmetric generalized non-linear sigma-models is constructed and scaling laws for the Green's functions near the critical point with only two independent critical exponents are established.     

Electrical conductivity of biphasic mixtures of molten silver iodide and lithium fluoride,chloride, and bromide

The electrical conductivity (EC) method was used for the biphasic systems of AgI with LiF, LiCl, or LiBr. The difference between the magnitudes of the conductivities for the equilibrium phases of the LiCl+AgI and LiBr+AgI melts decreases with an increase in temperature, becoming zero at 1250 and 983 K. For these temperatures, the values of critical conductivity are κ _c  = 4.70 S cm^?1 and κ _c  = 3.90 S cm^?1, respectively. The melt containing lithium fluoride exists in two phases up to a temperature of 1245 K. The temperature dependence of the differences between the conductivities for the coexisting phases is described as an exponential equation, with the critical exponent 0.89. This value is 11% less than that found for alkali halide melts. The covalent bonding between the silver and halide ions can be understood as causing the difference between the critical exponents of the alkali halide melts and those of silver iodide-containing mixtures.     

Dynamical simulations on the two-dimensional XY model with random-phase shift

Using resistively-shunted-junction dynamics, we numerically investigate the two-dimensional XY model with random phase shift. The critical temperatures and critical exponents are determined by dynamic scaling analysis. For weak disorder strengths, the system undergoes a Kosterlitz-Thouless (KT). A non-KT type phase transition is also observed for strong disorders. A genuine continuous depinning transition at zero temperature and creep motion at low temperature are also studied for various disorder strengths. The relevant critical currents and critical exponents are evaluated, and a non-Arrhenius creep motion is observed in the low temperature phases.     

Self-Similarity Breaking: Anomalous Nonequilibrium Finite-Size Scaling and Finite-Time Scaling

Symmetry breaking plays a pivotal role in modern physics.Although self-similarity is also a symmetry,and appears ubiquitously in nature,a fundamental question arises as to whether self-similarity breaking makes sense or not.Here,by identifying an important type of critical fluctuation,dubbed‘phases fluctuations’,and comparing the numerical results for those with self-similarity and those lacking self-similarity with respect to phases fluctuations,we show that self-similarity can indeed be broken,with significant consequences,at least in nonequilibrium situations.We find that the breaking of self-similarity results in new critical exponents,giving rise to a violation of the well-known finite-size scaling,or the less well-known finite-time scaling,and different leading exponents in either the ordered or the disordered phases of the paradigmatic Ising model on two-or three-dimensional finite lattices,when subject to the simplest nonequilibrium driving of linear heating or cooling through its critical point.This is in stark contrast to identical exponents and different amplitudes in usual critical phenomena.Our results demonstrate how surprising driven nonequilibrium critical phenomena can be.The application of this theory to other classical and quantum phase transitions is also anticipated.     

Universal critical exponent in class D superconductors

We study a physical system consisting of noninteracting quasiparticles in disordered superconductors that have neither time-reversal nor spin-rotation invariance. This system belongs to class D within the recent classification scheme of random matrix ensembles, and its phase diagram contains three different phases: metallic and two distinct localized phases with different quantized thermal Hall conductances. We find that critical exponents describing different transitions (insulator-to-insulator and insulator-to-metal) are identical within the error of numerical calculations and also find that critical disorder of the insulator-to-metal transition is energy-independent.     

The Domany-Kinzel cellular automaton phase diagram

The boundaries between the three phases of the Domany-Kinzel probabilistic cellular automaton are determined with high accuracy via the gradient method. The difficulties the extrapolation to the thermodynamic limit are circumvented and the critical exponents are also presented.     

一维自旋1键交替XXZ链中的量子纠缠和临界指数

利用基于张量网络表示的矩阵乘积态算法以及无限虚时间演化块抽取方法,本文研究了一维无限格点自旋1的键交替反铁磁XXZ海森伯模型中的量子相变.分别计算了系统的von Neumann熵、单位格点保真度和序参量,从而得到了系统随键交替强度的变化从拓扑有序Néel相到局域有序二聚化相的量子相变点.我们用矩阵乘积态方法拟合出了相变的中心荷c?0.5,表明此相变属于二维经典的Ising普适类.另外,通过对拓扑Néel序的数值拟合,我们得到了相变点处的特征临界指数β′=0.236和γ′=0.838.     

Critical phenomena of thick branes in warped spacetimes

We have investigated the effects of a generic bulk first-order phase transition on thick Minkowski branes in warped geometries. As occurs in Euclidean space, when the system is brought near the phase transition an interface separating two ordered phases splits into two interfaces with a disordered phase in between. A remarkable and distinctive feature is that the critical temperature of the phase transition is lowered due to pure geometrical effects. We have studied a variety of critical exponents and the evolution of the transverse-traceless sector of the metric fluctuations.     

Critical exponents predicted by grouping of Feynman diagrams in φ4 model

Different perturbation theory treatments of the Ginzburg‐Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical exponents consistent with the known exact solutions in two dimensions. The usual perturbation theory is reorganized by appropriate grouping of Feynman diagrams of φ⁴ model with O(n) symmetry. As a result, equations for calculation of the two‐point correlation function are obtained which allow to predict possible exact values of critical exponents in two and three dimensions by proving relevant scaling properties of the asymptotic solution at (and near) the criticality. The new values of critical exponents are discussed and compared to the results of numerical simulations and experiments.     

Nonuniversal ordering of spin and charge in stripe phases

We study the interplay of topological excitations in stripe phases: charge dislocations, charge loops, and spin vortices. In two dimensions these defects interact logarithmically on large distances. Using a renormalization-group analysis in the Coulomb-gas representation of these defects, we calculate the phase diagram and the critical properties of the transitions. Depending on the interaction parameters, spin and charge order can disappear at a single transition or in a sequence of two transitions (spin-charge separation). These transitions are nonuniversal with continuously varying critical exponents. We also determine the nature of the points where three phases coexist.     

A Unified Approach to the Thermodynamics and Quantum Scaling Functions of One-Dimensional Strongly Attractive SU(w) Fermi Gases

We present a unified derivation of the pressure equation of states, thermodynamics and scaling functions for the one-dimensional(1 D) strongly attractive Fermi gases with SU(w) symmetry. These physical quantities provide a rigorous understanding on a universality class of quantum criticality characterized by the critical exponents z=2 and correlation length exponent v=1/2. Such a universality class of quantum criticality can occur when the Fermi sea of one branch of charge bound states starts to fill or becomes gapped at zero temperature. The quantum critical cone can be determined by the double peaks in specific heat, which serve to mark two crossover temperatures fanning out from the critical point. Our method opens to further study on quantum phases and phase transitions in strongly interacting fermions with large SU(w) and non-SU(w) symmetries in one dimension.     

Statical critical properties of gadolinium models

Microscopic models of real ferromagnetic gadolinium are proposed, and their critical properties are studied by the Monte Carlo method. The critical exponents α (heat capacity), γ (susceptibility), and β (magnetization) are calculated. The α, β, and γ exponents are determined by the approximation of the data on the basis of traditional power functions and in the framework of the finite-size scaling theory. It is revealed that the critical behavior of gadolinium is affected by the dipole-dipole interactions. It is shown that the Monte Carlo method is a powerful tool for investigations into the critical properties of complex models in which two types of weak relativistic interactions are jointly taken into account against the background of each of these interactions.     

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.     

Critical behavior studies in Ti-substituted lanthanum bismuth perovskite manganites

Perovskite manganite La_0.4Bi_0.6Mn_1−xTi_xO₃ (x = 0.05 and 0.1) synthesized using conventional solid state route method give rise to critical phenomenon in their magnetic interactions due to the substitution of non magnetic Ti ions. The critical behavior is observed near paramagnetic–ferromagnetic transition and is studied by magnetization measurements. Various techniques like Modified Arrott plot, Kouvel–Fisher method, scaling equation of state analysis and the critical magnetization isotherm were used to analyze the magnetization data on magnetic phase transition. The values of critical exponents β and γ obtained using different techniques are in good agreement. The obtained critical exponents are found to follow scaling equation with the magnetization data scaled into two different curves below and above the transition temperature, T_C. This confirms that the critical exponents and T_C are reasonably accurate. The obtained critical exponents for both the samples deviates from mean-field model and do not completely follow the static long range ferromagnetic ordering. This behavior is consistent with non magnetic nature of Ti substituted at Mn site and can be associated with Griffiths phase like phenomenon.     

Nonlocal Kardar-Parisi-Zhang equation with spatially correlated noise

The effects of spatially correlated noise on a phenomenological equation equivalent to a nonlocal version of the Kardar-Parisi-Zhang (KPZ) equation are studied via the dynamic renormalization group (DRG) techniques. The correlated noise coupled with the long ranged nature of interactions prove the existence of different phases in different regimes, giving rise to a range of roughness exponents defined by their corresponding critical dimensions. Finally self-consistent mode analysis is employed to compare the non-KPZ exponents obtained as a result of the long-range interactions with the DRG results.     

Numerical renormalization-group study of the Bose-Fermi Kondo model

We extend the numerical renormalization-group method to Bose-Fermi Kondo models (BFKMs), describing a local moment coupled to a conduction band and a dissipative bosonic bath. We apply the method to the Ising-symmetry BFKM with a bosonic bath spectral function eta(omega) proportional omega(s), of interest in connection with heavy-fermion criticality. For 0 < s < 1, an interacting critical point, characterized by hyperscaling of exponents and omega/T scaling, describes a quantum phase transition between Kondo-screened and localized phases. A connection is made to other results for the BFKM and the spin-boson model.     

Exact results for the Kardar-Parisi-Zhang equation with spatially correlated noise

We investigate the Kardar-Parisi-Zhang (KPZ) equation in d spatial dimensions with Gaussian spatially long-range correlated noise -- characterized by its second moment -- by means of dynamic field theory and the renormalization group. Using a stochastic Cole-Hopf transformation we derive exact exponents and scaling functions for the roughening transition and the smooth phase above the lower critical dimension . Below the lower critical dimension, there is a line marking the stability boundary between the short-range and long-range noise fixed points. For , the general structure of the renormalization-group equations fixes the values of the dynamic and roughness exponents exactly, whereas above , one has to rely on some perturbational techniques. We discuss the location of this stability boundary in light of the exact results derived in this paper, and from results known in the literature. In particular, we conjecture that there might be two qualitatively different strong-coupling phases above and below the lower critical dimension, respectively. Received 5 August 1998     

Investigating the nonequilibrium aspects of long-range Potts model: Refinement of critical temperatures and raw exponents

In this work, we analyze the q-state Potts model with long-range interactions through nonequilibrium scaling relations commonly used when studying short-range systems. We determine the critical temperature via an optimization method for short-time Monte Carlo simulations. The study takes into consideration two different boundary conditions and three different values of range parameters of the couplings. We also present estimates of some critical exponents, named as raw exponents for systems with long-range interactions, which confirm the non-universal character of the model. Finally, we provide some preliminary results addressing the relations between the raw exponents and the exponents obtained for systems with short-range interactions. The results assert that the methods employed in this work are suitable to study the considered model and can easily be adapted to other systems with long-range interactions.