Critical Behavior of Light

Light is shown to exhibit critical and tricritical behavior in passive mode-locked lasers with externally injected pulses. It is a first and unique example of critical phenomena in a one-dimensional many body light-mode system. The phase diagrams consist of regimes with continuous wave, driven para-pulses, spontaneous pulses via mode condensation, and heterogeneous pulses, separated by phase transition lines which terminate with critical or tricritical points. Enhanced nongaussian fluctuations and collective dynamics are observed at the critical and tricritical points, showing a mode system analog of the critical opalescence phenomenon. The critical exponents are calculated and shown to comply with the mean field theory, which is rigorous in the light system.Comment: RevTex, 5 pages, 3 figure

Critical behavior in Angelesco ensembles

We consider Angelesco ensembles with respect to two modified Jacobi weights on touching intervals [a,0] and [0,1], for a < 0. As a \to -1 the particles around 0 experience a phase transition. This transition is studied in a double scaling limit, where we let the number of particles of the ensemble tend to infinity while the parameter a tends to -1 at a rate of order n^{-1/2}. The correlation kernel converges, in this regime, to a new kind of universal kernel, the Angelesco kernel K^{Ang}. The result follows from the Deift/Zhou steepest descent analysis, applied to the Riemann-Hilbert problem for multiple orthogonal polynomials.Comment: 32 pages, 9 figure

Critical behavior of Griffiths ferromagnets

From a heuristic calculation of the leading order essential singularity in the distribution of Yang-Lee zeroes, we obtain new scaling relations near the ferromagnetic-Griffiths transition, including the prediction of a discontinuity on the analogue of the critical isotherm. We show that experimental data for the magnetization and heat capacity of $\mathrm{La_{0.7}Ca_{0.3}MnO_3}$ are consistent with these predictions, thus supporting its identification as a Griffiths ferromagnet.Comment: 4 pages, 3 figures, Changed conten

Quantum Critical Behavior in Kondo Systems

This article briefly reviews three topics related to the quantum critical behavior of certain heavy-fermion systems. First, we summarize an extended dynamical mean-field theory for the Kondo lattice, which treats on an equal footing the quantum fluctuations associated with the Kondo and RKKY couplings. The dynamical mean-field equations describe an effective Kondo impurity model with an additional coupling to vector bosons. Two types of quantum phase transition appear to be possible within this approach---the first a conventional spin-density-wave transition, the second driven by local physics. For the second type of transition to be realized, the effective impurity model must have a quantum critical point exhibiting an anomalous local spin susceptibility. In the second part of the paper, such a critical point is shown to occur in two variants of the Kondo impurity problem. Finally, we propose an operational test for the existence of quantum critical behavior driven by local physics. Neutron scattering results suggest that CeCu$_{6-x}$Au$_x$ passes this test.Comment: 6 pages, 4 eps figures, REVTeX (epsf style

Critical behavior of CrTe1-xSbx ferromagnet

The modified Arrott plots and Kouvel${\text -}$Fisher analysis are used to investigate the critical behavior of $CrTe_{1-x}Sb_{x}$ ferromagnetic material near its transition temperature $T_{c}$. The Ferro${\text -}$Paramagnetic transition is found to be a second${\text -}$order phase transition. For $x=0.2$, the critical exponents closely follow the Mean Field Model with the estimated values of the exponents: $\beta$ =0.60 $\pm$ 0.03, $\gamma$ =1.00 $\pm$ 0.03 and $\delta$ =2.67 $\pm$ 0.03. We also found with increasing Sb${\text -}$concentrations, the critical exponents significantly deviate from the mean field values and gradually shift towards the 3${\text -}$Dimensional behavior. The deviation may indicate changes in the spin configuration with increasing Sb concentrations

Crossover critical behavior of Ga1-xMnxAs

The critical behavior of Ga1-xMnxAs in a close vicinity of the Curie temperature was experimentally studied by using the thermal diffusivity measurements. Taking into account that the inverse of the thermal diffusivity has the same critical behavior as the specific heat, the critical exponent {\alpha} for the samples investigated has been determined. With approaching close to the critical temperature, the crossover from the mean-field-like to the Ising-like critical behavior has been observed. From the crossover behavior the values of the Ginzburg number and the exchange interaction length in Ga1-xMnxAs with different concentrations of Mn were determined.Comment: 17 pages, 5 figure

Depth-dependent critical behavior in V2H

Using X-ray diffuse scattering, we investigate the critical behavior of an order-disorder phase transition in a defective "skin-layer" of V2H. In the skin-layer, there exist walls of dislocation lines oriented normal to the surface. The density of dislocation lines within a wall decreases continuously with depth. We find that, because of this inhomogeneous distribution of defects, the transition effectively occurs at a depth-dependent local critical temperature. A depth-dependent scaling law is proposed to describe the corresponding critical ordering behavior.Comment: 5 pages, 4 figure