Bulk and boundary critical behavior at Lifshitz points

Lifshitz points are multicritical points at which a disordered phase, a homogeneous ordered phase, and a modulated ordered phase meet. Their bulk universality classes are described by natural generalizations of the standard φ⁴ model. Analyzing these models systematically via modern field-theoretic renormalization group methods has been a long-standing challenge ever since their introduction in the middle of 1970s. We survey the recent progress made in this direction, discussing results obtained via dimensionality expansions, how they compare with Monte Carlo results, and open problems. These advances opened the way towards systematic studies of boundary critical behavior atm-axial Lifshitz points. The possible boundary critical behavior depends on whether the surface plane is perpendicular to one of them modulation axes or parallel to all of them. We show that the semi-infinite field theories representing the corresponding surface universality classes in these two cases of perpendicular and parallel surface orientation differ crucially in their Hamiltonian’s boundary terms and the implied boundary conditions, and explain recent results along with our current understanding of this matter.     

Field theory of critical behavior in a driven diffusive system

Journal of Statistical Physics -     

Field theory of critical behavior in a driven diffusive system

We use a field theoretic renormalization group method to study the critical properties of a diffusive system with a single conserved density subject to a constant uniform external field. A fixed point stable belowd _c=5 is found to govern the critical behavior. Scaling forms of density correlation functions are derived and critical exponents are obtained to all orders in =5–d. Spatial correlations are found to be very anisotropic with elongated correlations along the external field. Long wavelength transverse fluctuations are suppressed completely to yield mean field transverse exponents.     

Reaction-diffusion system with self-organized critical behavior

We describe the construction of a conserved reaction-diffusion system that exhibits self-organized critical (avalanche-like) behavior under the action of a slow addition of particles. The model provides an illustration of the general mechanism to generate self-organized criticality in conserving systems. Extensive simulations in d = 2 and 3 reveal critical exponents compatible with the universality class of the stochastic Manna sandpile model. Received 16 November 2000     

Phase equilibria,metastable states,and critical points in a simple one-component system

Stability of metastable phase states against infinitesimal perturbations in a simple one-component system is considered. The method of molecular dynamics simulation was used to determine the boundaries of essential instability of supersaturated vapor, a superheated liquid, and a superheated crystal. The absence of a spinodal from a supercooled liquid and the dependence of the boundary of essential instability of a superheated crystal on the character of deformation were established. It is shown that each of the three lines of phase equilibria in a one-component system has an endpoint of termination of phase coexistence. As distinct from the liquid–gas critical point, which is the point of phase identity and is located in the region of stable states, the endpoints of melting and sublimation lines are located in the region ofmetastable states. At these points, a critical (spinodal) state is achieved only for one of the coexisting phases.     

Robustness of heterogeneous complex networks

In this paper we study the robustness of heterogeneous preferential attachment networks. The robustness of a network measures its structural tolerance to the random removal of nodes and links. We numerically analyze the influence of the affinity parameters on a set of ensemble-averaged robustness metrics. We show that the presence of heterogeneity does not fundamentally alter the smooth nature of the fragmentation process of the models. We also show that a moderate level of locality translates into slight improvements in the robustness metrics, which prompts us to conjecture an evolutionary argument for the existence of real networks with power-law scaling in their connectivity and clustering distributions.     

Quenched disorder and the critical behavior of a partially frustrated system

We report the direct observation of the effects of quenched disorder on the critical behavior of partially frustrated amorphous FeMnZr alloys by the systematic analysis of high-precision ac susceptibility data and dc magnetization data. Interestingly, the analysis reveals that the presence of short-range quenched disorder does not alter the actual critical behavior. However, it does affect quantities such as the Curie temperature, the peak value of effective exponent gamma, width of the peak, and crossover temperatures. The observed temperature dependence of the effective critical exponent can be understood in terms of the field-theoretical renormalization group approach. Also, the present results would help in identifying the main source of the spread in the exponent values reported in the literature.     

Bulk singularities at critical end points: a field-theory analysis

A class of continuum models with a critical end point is considered whose Hamiltonian [φ,ψ] involves two densities: a primary order-parameter field, φ, and a secondary (noncritical) one, ψ. Field-theoretic methods (renormalization group results in conjunction with functional methods) are used to give a systematic derivation of singularities occurring at critical end points. Specifically, the thermal singularity ∼ | t|^{2 - α} of the first-order line on which the disordered or ordered phase coexists with the noncritical spectator phase, and the coexistence singularity ∼ | t|^{1 - α} or ∼ | t|^β of the secondary density <ψ> are derived. It is clarified how the renormalization group (RG) scenario found in position-space RG calculations, in which the critical end point and the critical line are mapped onto two separate fixed points _CEP ^* and _λ ^*, translates into field theory. The critical RG eigenexponents of _CEP ^* and _λ ^* are shown to match. _CEP ^* is demonstrated to have a discontinuity eigenperturbation (with eigenvalue y = d), tangent to the unstable trajectory that emanates from _CEP ^* and leads to _λ ^*. The nature and origin of this eigenperturbation as well as the role redundant operators play are elucidated. The results validate that the critical behavior at the end point is the same as on the critical line. Received 18 January 2001     

Landau-Zener transition of a two-level system driven by spin chains near their critical points

The Landau-Zener (LZ) transition of a two-level system coupling to spin chains near their critical points is studied in this paper. Two kinds of spin chains, the Ising spin chain and XY spin chain, are considered. We calculate and analyze the effects of system-chain coupling on the LZ transition. A relation between the LZ transition and the critical points of the spin chain is established. These results suggest that LZ transitions may serve as the witnesses of criticality of the spin chain. This may provide a new way to study quantum phase transitions as well as LZ transitions.     

Effects of turbulent mixing on the critical behavior

Effects of strongly anisotropic turbulent mixing on the critical behavior are studied by means of the renormalization group. Existence of new nonequilibrium types of critical regimes (universality classes) is established.     

Bimodality: a sign of critical behavior in nuclear reactions

The recently discovered coexistence of multifragmentation and residue production for the same total transverse energy of light charged particles, which has been dubbed bimodality like it has been introduced in the framework of equilibrium thermodynamics, can be well reproduced in numerical simulations of heavy ion reactions. A detailed analysis shows that fluctuations (introduced by elementary nucleon-nucleon collisions) determine which of the exit states is realized. Thus, we can identify bifurcation in heavy ion reactions as a critical phenomenon. Also the scaling of the coexistence region with beam energy is well reproduced in these results from the quantum molecular dynamics simulation program.     

Simulation of critical fluid Rayleigh linewidth behavior by a normal fluid system

The dynamic droplet model of a critical fluid provides a simple physical model of a critical fluid. We use this to model an emulsion which mimics the Rayleigh linewidth behavior of a critical fluid in the nonhydrodynamic regime.     

Robustness of optimal working points for nonadiabatic holonomic quantum computation

Geometric phases are an interesting resource for quantum computation in view of their robustness against decoherence effects. We study the effects of the environment on a class of one-qubit holonomic gates that have recently been shown to be characterized by “optimal” working times. We numerically analyze the behavior of these optimal points and focus on their robustness against noise.     

Detection of quantum critical points by a probe qubit

Quantum phase transitions occur when the ground state of a quantum system undergoes a qualitative change when an external control parameter reaches a critical value. Here, we demonstrate a technique for studying quantum systems undergoing a phase transition by coupling the system to a probe qubit. It uses directly the increased sensibility of the quantum system to perturbations when it is close to a critical point. Using an NMR quantum simulator, we demonstrate this measurement technique for two different types of quantum phase transitions in an Ising spin chain.     

Robustness of the bistable behavior of a biological signaling feedback loop

Biological signaling networks comprised of cellular components including signaling proteins and small molecule messengers control the many cell function in responses to various extracellular and intracellular signals including hormone and neurotransmitter inputs, and genetic events. Many signaling pathways have motifs familiar to electronics and control theory design. Feedback loops are among the most common of these. Using experimentally derived parameters, we modeled a positive feedback loop in signaling pathways used by growth factors to trigger cell proliferation. This feedback loop is bistable under physiological conditions, although the system can move to a monostable state as well. We find that bistability persists under a wide range of regulatory conditions, even when core enzymes in the feedback loop deviate from physiological values. We did not observe any other phenomena in the core feedback loop, but the addition of a delayed inhibitory feedback was able to generate oscillations under rather extreme parameter conditions. Such oscillations may not be of physiological relevance. We propose that the kinetic properties of this feedback loop have evolved to support bistability and flexibility in going between bistable and monostable modes, while simultaneously being very refractory to oscillatory states. (c) 2001 American Institute of Physics.     

Sound velocity dispersion in a solution with two critical points

The dispersion of the sound velocity in a solution with a region of stratification has been investigated experimentally in the frequency range from 2.6 MHz to 12 GHz. It is found that the dispersion of the sound velocity below the lower critical temperature of stratification reaches 22% and depends linearly to the temperature above the upper critical temperature of separation, the dispersion of the sound velocity is much smaller and has a different linear dependence on the temperature. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 3, 166–168 (10 August 1996)