External field dependence of the correlation lengths in the three-dimensional O(4) model

We investigate numerically the transverse and longitudinal correlation lengths of the three-dimensional O(4) model as a function of the external field H. In the low-temperature phase we verify explicitly the H^{-1/2}-dependence of the transverse correlation length, which is expected due to the Goldstone modes of the model. On the critical line we find the universal amplitude ratio xi^c_T / xi^c_L = 1.99(1). From our data we derive the universal scaling function for the transverse correlation length. The H-dependencies of the correlation lengths in the high temperature phase are discussed and shown to be in accord with the scaling functions.Comment: 3 pages, 4 figures, Lattice2003(higgs) contribution, espcrc2.st

The transition temperature of the dilute interacting Bose gas

We show that the critical temperature of a uniform dilute Bose gas must increase linearly with the s-wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations.Comment: 4 pages, Revtex, to be published in Physical Review Letter

Gauge theory description of glass transition

An analytical approach, which develops the gauge model of the glass transition phenomenon, is suggested. It is based on the quantum field theory and critical dynamics methods. The suggested mechanism of glass transition is based on the interaction of the local magnetization field with the massive gauge field, which describes frustration-induced plastic deformation. The example of the three-dimensional Heisenberg model with trapped disorder is considered. It is shown that the glass transition appears when the fluctuations scale reaches the frustrations scale, and the mass of the gauge field becomes equal to zero. The Vogel-Fulcher-Tammann relation for the glass transition kinetics and critical exponent for non-linear susceptibility, $1.7\lesssim \gamma < 3$, are derived in the framework of the suggested approach.Comment: 4 pages, 4 figures; Added references; correction

Longitudinal and transverse spectral functions in the three-dimensional O(4) model

We have performed a high statistics simulation of the O(4) model on a three-dimensional lattice of linear extension L=120 for small external fields H. Using the maximum entropy method we analyze the longitudinal and transverse plane spin correlation functions for T=T_c. In the transverse case we find for all T and H a single sharp peak in the spectral function, whose position defines the transverse mass m_T, the correlator is that of a free particle with mass m_T. In the longitudinal case we find in the very high temperature region also a single sharp peak in the spectrum. On approaching the critical point from above the peak broadens somewhat and at T_c its position m_L is at 2m_T for all our H-values. Below T_c we find still a significant peak at omega=2m_T and at higher omega-values a continuum of states with several smaller peaks with decreasing heights. This finding is in accord with a relation of Patashinskii and Pokrovskii between the longitudinal and the transverse correlation functions. We test this relation in the following. As a by-product we calculate critical exponents and amplitudes and confirm our former results.Comment: 38 pages, 26 figure

Critical phenomena on scale-free networks: logarithmic corrections and scaling functions

In this paper, we address the logarithmic corrections to the leading power laws that govern thermodynamic quantities as a second-order phase transition point is approached. For phase transitions of spin systems on d-dimensional lattices, such corrections appear at some marginal values of the order parameter or space dimension. We present new scaling relations for these exponents. We also consider a spin system on a scale-free network which exhibits logarithmic corrections due to the specific network properties. To this end, we analyze the phase behavior of a model with coupled order parameters on a scale-free network and extract leading and logarithmic correction-to-scaling exponents that determine its field- and temperature behavior. Although both non-trivial sets of exponents emerge from the correlations in the network structure rather than from the spin fluctuations they fulfil the respective thermodynamic scaling relations. For the scale-free networks the logarithmic corrections appear at marginal values of the node degree distribution exponent. In addition we calculate scaling functions, which also exhibit nontrivial dependence on intrinsic network properties.Comment: 15 pages, 4 figure

Universal amplitude ratios from numerical studies of the three-dimensional O(2) model

We investigate the three-dimensional O(2) model near the critical point by Monte Carlo simulations and calculate the major universal amplitude ratios of the model. The ratio U_0=A+/A- is determined directly from the specific heat data at zero magnetic field. The data do not, however, allow to extract an accurate estimate for alpha. Instead, we establish a strong correlation of U_0 with the value of alpha used in the fit. This numerical alpha-dependence is given by A+/A- = 1 -4.20(5) alpha + O(alpha^2). For the special alpha-values used in other calculations we find full agreement with the corresponding ratio values, e. g. that of the shuttle experiment with liquid helium. On the critical isochore we obtain the ratio xi+/xi-_T=0.293(9), and on the critical line the ratio xi_T^c/xi_L^c=1.957(10) for the amplitudes of the transverse and longitudinal correlation lengths. These two ratios are independent of the used alpha or nu-values.Comment: 34 pages, 19 Ps-figures, Latex2e, revised version, to be published in J. Phys.

Nonequilibrium Critical Phenomena

We discuss the non-equilibrium critical phenomena in liquids, and the models for these phenomena based on local equilibrium and extended scaling assumptions. Special situations are proposed for experimental tests of the theory. Near-critical steady and transient states are reviewed. In a near-critical steady state characterized by a temperature gradient, the theory predicts strong nonequilibrium fluctuations at very large length scales. Close to the critical point, this results in a nonlinear regime of heat conductivity. A transient non-equilibrium state triggered by a rapid and large spatially uniform perturbation of the critical liquid is considered. A step away from criticality generates a free field with strong and decaying correlations in initial state, while a step towards criticality initiates the increase of fluctuations and of their correlation at the large scale edge of the critical range. The approach to equilibrium is characterized by an equilibration length \Lambda_eq that depends on time t. The theory predicts a power law approach of the temperature to the new equilibrium; the new critical exponents depend on whether the temperature is initially increased or decreased

Non-equilibrium Characterization of Spinodal Points using Short Time Dynamics

Though intuitively appealing, the concept of spinodal is rigourously defined only in systems with infinite range interactions (mean field systems). In short-range systems, a pseudo-spinodal can be defined by extrapolation of metastable measurements, but the point itself is not reachable because it lies beyond the metastability limit. In this work we show that a sensible definition of spinodal points can be obtained through the short time dynamical behavior of the system deep inside the metastable phase, by looking for a point where the system shows critical behavior. We show that spinodal points obtained by this method agree both with the thermodynamical spinodal point in mean field systems and with the pseudo-spinodal point obtained by extrapolation of meta-equilibrium behavior in short range systems. With this definition, a practical determination can be achieved without regard for equilibration issues.Comment: 10 pages, 12 figure

Condensate density of interacting bosons: a functional renormalization group approach

We calculate the temperature dependent condensate density $\rho^0 (T)$ of interacting bosons in three dimensions using the functional renormalization group (FRG). From the numerical solution of suitably truncated FRG flow equations for the irreducible vertices we obtain $\rho^0 (T)$ for arbitrary temperatures. We carefully extrapolate our numerical results to the critical point and determine the order parameter exponent $\beta \approx 0.32$, in reasonable agreement with the expected value $0.345$ associated with the XY-universality class. We also calculate the condensate density in two dimensions at zero temperature using a truncation of the FRG flow equations based on the derivative expansion including cubic and quartic terms in the expansion of the effective potential in powers of the density. As compared with the widely used quadratic approximation for the effective potential, the coupling constants associated with the cubic and quartic terms increase the result for the condensate density by a few percent. However, the cubic and quartic coupling constants flow to rather large values, which sheds some doubt on FRG calculations based on a low order polynomial approximation for the effective potential.Comment: 9 pages, 6 figure

Controlled transport of solitons and bubbles using external perturbations

We investigate generalized soliton-bearing systems in the presence of external perturbations. We show the possibility of the transport of solitons using external waves, provided the waveform and its velocity satisfy certain conditions. We also investigate the stabilization and transport of bubbles using external perturbations in 3D-systems. We also present the results of real experiments with laser-induced vapor bubbles in liquids.Comment: 26 pages, 24 figure