Freezing of dynamical exponents in low dimensional random media

A particle in a random potential with logarithmic correlations in dimensions d = 1,2 is shown to undergo a dynamical transition at T(dyn)>0. In d = 1 exact results show T(dyn) = T(c), the static glass transition temperature, and that the dynamical exponent changes from z(T) = 2+2(T(c)/T)(2) at high T to z(T) = 4T(c)/T in the glass phase. The same formulas are argued to hold in d = 2. Dynamical freezing is also predicted in the 2D random gauge XY model and related systems. In d = 1 a mapping between dynamics and statics is unveiled and freezing involves barriers as well as valleys. Anomalous scaling occurs in the creep dynamics, relevant to dislocation motion experiments.     

Calculation of partition functions by measuring component distributions

A new algorithm is presented, which allows us to calculate numerically the partition function Z for systems, which can be described by arbitrary interaction graphs and lattices, e.g., Ising models or Potts models (for arbitrary values q>0), including random or diluted models. The new approach is suitable for large systems. The basic idea is to measure the distribution of the number of connected components in the corresponding Fortuin-Kasteleyn representation and to compare with the case of zero degrees of freedom, where the exact result Z=1 is known. As an application, d=2 and d=3 dimensional ferromagnetic Potts models are studied, and the critical values qc, where the transition changes from second to first order, are determined. Large systems of sizes N=1000(2) and N=100(3) are treated. The critical value qc(d=2)=4 is confirmed and qc(d=3)=2.35(5) is found.     

Universality of synchrony: critical behavior in a discrete model of stochastic phase-coupled oscillators

We present the simplest discrete model to date that leads to synchronization of stochastic phase-coupled oscillators. In the mean field limit, the model exhibits a Hopf bifurcation and global oscillatory behavior as coupling crosses a critical value. When coupling between units is strictly local, the model undergoes a continuous phase transition which we characterize numerically using finite-size scaling analysis. In particular, the onset of global synchrony is marked by signatures of the XY universality class, including the appropriate classical exponents beta and nu, a lower critical dimension d(lc) = 2, and an upper critical dimension d(uc) = 4.     

Global nature of dilute-to-dense transition of granular flows in a 2D channel

The dilute-to-dense transition of granular flow of particle size d(0) is studied experimentally in a two-dimensional channel (width D) with confined exit (width d). Our results show that with fixed d and D there is a maximum inflow rate Q(c) above which the flow changes from dilute to dense and the outflow rate drops abruptly from Q(c) to a dense rate Q(d). A rescaled critical rate q(c) is found to be a function of a scaling variable lambda only: q(c) approximately F(lambda), where lambda identical with d/d(0) d/D-d. This form of lambda suggests that the dilute-to-dense transition is a global property of the flow, unlike the jamming transition which depends only on d/d(0). Furthermore, the transition is found to occur when the area fraction of particles near the exit exceeds a critical value which is close to 0.65+/-0.03.     

Clique percolation in random networks

The notion of k-clique percolation in random graphs is introduced, where k is the size of the complete subgraphs whose large scale organizations are analytically and numerically investigated. For the Erdos-Rényi graph of N vertices we obtain that the percolation transition of k-cliques takes place when the probability of two vertices being connected by an edge reaches the threshold p(c) (k) = [(k - 1)N](-1/(k - 1)). At the transition point the scaling of the giant component with N is highly nontrivial and depends on k. We discuss why clique percolation is a novel and efficient approach to the identification of overlapping communities in large real networks.     

Random walks on a ( 2+1)-dimensional deformable medium

A model of random walks on a deformable medium is proposed in 2+1 dimensions. The behavior of the walk is characterized by the stability parameter beta and the stiffness exponent alpha. The average square end-to-end distance l approximately equals (2nu) and the average number of visited sites approximately equals (k) are calculated. As beta increases, for each alpha there exists a critical transition point beta(c) from purely random walks ( nu = 1/2 and k approximate to 1) to compact growth ( nu = 1/3 and k = 2/3). The relationship between beta(c) and alpha can be expressed as beta(c) = e(alpha). The landscape generated by a walk is also investigated by means of the visit-number distribution N(n)(beta). There exists a scaling relationship of the form N(n)(beta)approximately n(-2)f(n/beta(z)).     

Rounding by disorder of first-order quantum phase transitions: emergence of quantum critical points

We give a heuristic argument for disorder rounding of a first-order quantum phase transition into a continuous phase transition. From both weak and strong disorder analysis of the N-color quantum Ashkin-Teller model in one spatial dimension, we find that, for N > or =3, the first-order transition is rounded to a continuous transition and the physical picture is the same as the random transverse field Ising model for a limited parameter regime. The results are strikingly different from the corresponding classical problem in two dimensions where the fate of the renormalization group flows is a fixed point corresponding to N-decoupled pure Ising models.     

The d-dimensional sine-Gordon model in the presence of random fields

We study the properties of a d-dimensional sine-Gordon model in the presence of a random field that couples linearly to the sine-Gordon field using the Wilson renormalization group approach via the replica trick. No stable fixed point is found for dimensionalities d<4, corresponding to the absence of long-range order. Such a situation seems to occur in experiments on impurity-pinned charge-density-wave systems in which a “glassy behaviour” appears to be induced by arbitrarily weak symmetry-breaking randomness.     

Short-Time Dynamics of the Random n-Vector Model

Short-time critical behavior of the random n-vector model is studied by the theoretic renormalization-group approach.Asymptotic scaling laws are studied in a frame of the expansion in ε = 4 - d for n ≠ 1 and √ε for n = 1respectively.In d ＜ 4,the initial slip exponents θ′ for the order parameter and θ for the response function are calculated up to the second order in ε ＝ 4 - d for n ≠ 1 and √ε for n ＝ 1 at the random fixed point respectively.Our results show that the random impurities exert a strong influence on the short-time dynamics for d ＜ 4 and n ＜ n_c.     

Swelling-collapse transition of self-attracting walks

We study the structural properties of self-attracting walks in d dimensions using scaling arguments and Monte Carlo simulations. We find evidence of a transition analogous to the Theta transition of polymers. Above a critical attractive interaction u(c), the walk collapses and the exponents nu and k, characterizing the scaling with time t of the mean square end-to-end distance approximately t(2nu) and the average number of visited sites approximately t(k), are universal and given by nu=1/(d+1) and k=d/(d+1). Below u(c), the walk swells and the exponents are as with no interaction, i.e., nu=1/2 for all d, k=1/2 for d=1 and k=1 for d>/=2. At u(c), the exponents are found to be in a different universality class.     

From Continuous to First Order Phase Transition in a Generalized XY Model

A generalized XY model with interaction V(θ) = 2 J{1 - [cos² (θ/2)]^p2} is studied by Monte Carlo renormalization group method on two-dimensional random triangle lattice. For p = √2, a line of fixed points has been found. It characterizes that there is a Kosterlitz-Thouless phase transition. For p = 2, a first order phase transition has been found. Both of them show the relationship between the nature of phase transition and the class of interactions.     

Complexity of random energy landscapes, glass transition, and absolute value of the spectral determinant of random matrices

Finding the mean of the total number N(tot) of stationary points for N-dimensional random energy landscapes is reduced to averaging the absolute value of the characteristic polynomial of the corresponding Hessian. For any finite N we provide the exact solution to the problem for a class of landscapes corresponding to the "toy model" of manifolds in a random environment. For N>1 our asymptotic analysis reveals a phase transition at some critical value mu(c) of a control parameter mu from a phase with a finite landscape complexity: N(tot) approximately e(N Sigma), Sigma(mu0 to the phase with vanishing complexity: Sigma(mu>mu(c))=0. Finally, we discuss a method of dealing with the modulus of the spectral determinant applicable to a broad class of problems.     

Isotropic phase of nematics in porous media

We study the effect of random porous matrices on the isotropic-nematic phase transition. Sufficiently close to the cleaning temperature, both random field and thermal fluctuations are important as disordering agents. A novel random field fixed point of the renormalization group equation was found that controls the transition from isotropic to the replica symmetric phase. Explicit evaluation of the exponents in d = 6 ? ε dimensions yields to a dimensional reduction and three-exponent scaling.     

Magnetic and electronic phase transitions and magnetoresistance effect in the Pr0.5−xLaxSr0.5MnO3 (, 0.15) system

The electronic and magnetic phase transitions of Pr_0.5−xLa_xSr_0.5MnO₃ with x=0.10 and 0.15 were investigated. The M(T) and ρ(T) curves for these samples clearly show transitions from antiferromagnetic insulator to ferromagnetic semiconductor, ferromagnetic metal and finally to paramagnetic semiconductor as the temperature is increased from 5 to 300 K. Especially, two obvious protrudent peaks in the magnetoresistance curves MR(T) for these samples were clearly observed in the relative low magnetic field, 1 T. One peak appears at around the antiferromagnet-ferromagnet transition temperature T_N (150 K) with MR≈−23%, another occurs at around the ferromagnet-paramagnet transition temperature T_C(275 K ) with MR≈−8.2%. In addition, when the magnetic field was increased, the temperature corresponding to the MR peak at T_N shifts to lower temperature while the temperature corresponding to the MR peak at T_C is fixed.     

Spin glasses on thin graphs

In a recent paper [C. Baillie, D.A. Johnston and J.-P. Kownacki, Nucl. Phys. B 432 (1994) 551] we found strong evidence from simulations that the Ising antiferromagnet on “thin” random graphs — Feynman diagrams — displayed a mean-field spin-glass transition. The intrinsic interest of considering such random graphs is that they give mean-field theory results without long-range interactions or the drawbacks, arising from boundary problems, of the Bethe lattice. In this paper we reprise the saddle-point calculations for the Ising and Potts ferromagnet, antiferromagnet and spin glass on Feynman diagrams. We use standard results from bifurcation theory that enable us to treat an arbitrary number of replicas and any quenched bond distribution. We note the agreement between the ferromagnetic and spin-glass transition temperatures thus calculated and those derived by analogy with the Bethe lattice or in previous replica calculations.

We then investigate numerically spin glasses with a ±J bond distribution for the Ising and Q = 3, 4, 10, 50 state Potts models, paying particular attention to the independence of the spin-glass transition from the fraction of positive and negative bonds in the Ising case and the qualitative form of the overlap distribution P(q) for all of the models. The parallels with infinite-range spin-glass models in both the analytical calculations and simulations are pointed out.     

Exotic versus conventional scaling and universality in a disordered bilayer quantum heisenberg antiferromagnet

We present Monte Carlo simulations of a two-dimensional bilayer quantum Heisenberg antiferromagnet with random dimer dilution. In contrast with exotic scaling scenarios found in other random quantum systems, the quantum phase transition in this system is characterized by a finite-disorder fixed point with power-law scaling. After accounting for corrections to scaling, with a leading irrelevant exponent of omega approximately 0.48, we find universal critical exponents z=1.310(6) and nu=1.16(3). We discuss the consequences of these findings and suggest new experiments.     

Critical behavior in the vicinity of nematic to smectic A (N–SmA) phase transition of two polar–polar binary liquid crystalline systems

Phase diagram, critical behavior and order of the nematic (N)–smectic A (SmA) phase transition of two polar–polar binary systems (i) 4-n-heptyloxy-4′-cyanobiphenyl (7OCB) and 4-n-octyloxy-4′-cyanobiphenyl (8OCB); (ii) 4-n-octyloxy-4′-cyanobiphenyl (8OCB) and 4-n-nonyloxy-4′-cyanobiphenyl (9OCB) by means of a high-resolution temperature scanning measurement of birefringence have been reported in this work. A simple power law analysis has been adopted to extract the specific heat critical exponent (α′) at N–SmA transition from birefringence data. The α′ for N–SmA transition indicates a uniform crossover behavior and has appeared to be non-universal in nature. With increasing concentration of the higher homologues for both the binary systems, the N–SmA transition reveals a strong tendency to be driven towards the tricritical nature. The 3D-XY limit (i.e. α′ = ?0.007) for N–SmA transition reaches at the concentration x_8OCB = 0.28 corresponding to the McMillan ratio 0.914, whereas the tricritical point has been found to appear near x_9OCB = 1.0 corresponding to McMillan ratio 0.992.     

Statics and dynamics of incommensurate spin order in a geometrically frustrated antiferromagnet CdCr2O4

Using elastic and inelastic neutron scattering we show that a cubic spinel, CdCr2O4, undergoes an elongation along the c axis (c > a = b) at its spin-Peierls-like phase transition at T(N) = 7.8 K. The Néel phase (T < T(N)) has an incommensurate spin structure with a characteristic wave vector Q(M) = (0, delta,1) with delta approximately 0.09 and with spins lying on the ac plane. This is in stark contrast to another well-known Cr-based spinel, ZnCr2O4, that undergoes a c-axis contraction and a commensurate spin order. The magnetic excitation of the incommensurate Néel state has a weak anisotropy gap of 0.6 meV and it consists of at least three bands extending up to 5 meV.     

Quantum superconductor-metal transition in a proximity array

A theory of the zero-temperature superconductor-metal transition is developed for an array of superconductive islands (of size d) coupled via a disordered two-dimensional conductor with the dimensionless conductance g = Planck's over 2 pi/e(2)R(square)>1. At T = 0 the macroscopically superconductive state of the array with lattice spacing b>d is destroyed at g相似文献   

Antiferromagnetic spin fluctuations above the dome-shaped and full-gap superconducting states of LaFeAsO1-xFx revealed by (75)As-nuclear quadrupole resonance

We report a systematic study by (75)As nuclear-quadrupole resonance in LaFeAsO(1-x)F(x). The antiferromagnetic spin fluctuation found above the magnetic ordering temperature T(N) = 58 K for x = 0.03 persists in the regime 0.04 ≤ x ≤ 0.08, where superconductivity sets in. A dome-shaped x dependence of the superconducting transition temperature T(c) is found, with the highest T(c) = 27 K at x = 0.06, which is realized under significant antiferromagnetic spin fluctuation. With increasing x further, the antiferromagnetic spin fluctuation decreases, and so does T(c). These features resemble closely the cuprates La(2-x)Sr(x)CuO(4). In x = 0.06, the spin-lattice relaxation rate (1/T(1)) below T(c) decreases exponentially down to 0.13T(c), which unambiguously indicates that the energy gaps are fully opened. The temperature variation of 1/T(1) below T(c) is rendered nonexponential for other x by impurity scattering.