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

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

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.

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

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

Infrared behavior in systems with a broken continuous symmetry: classical O(N) model vs interacting bosons

In systems with a spontaneously broken continuous symmetry, the perturbative loop expansion is plagued with infrared divergences due to the coupling between transverse and longitudinal fluctuations. As a result the longitudinal susceptibility diverges and the self-energy becomes singular at low energy. We study the crossover from the high-energy Gaussian regime, where perturbation theory remains valid, to the low-energy Goldstone regime characterized by a diverging longitudinal susceptibility. We consider both the classical linear O($N$) model and interacting bosons at zero temperature, using a variety of techniques: perturbation theory, hydrodynamic approach (i.e., for bosons, Popov's theory), large-$N$ limit and non-perturbative renormalization group. We emphasize the essential role of the Ginzburg momentum scale $p_G$ below which the perturbative approach breaks down. Even though the action of (non-relativistic) bosons includes a first-order time derivative term, we find remarkable similarities in the weak-coupling limit between the classical O($N$) model and interacting bosons at zero temperature.Comment: v2) 19 pages, 8 figure

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

Two-band superconductors: Hidden criticality deep in the superconducting state

We show that two-band superconductors harbor hidden criticality deep in the superconducting state, stemming from the critical temperature of the weaker band taken as an independent system. For sufficiently small interband coupling $\gamma$ the coherence length of the weaker band exhibits a remarkable deviation from the conventional monotonic increase with temperature, namely, a pronounced peak close to the hidden critical point. The magnitude of the peak scales proportionally to \gamma^(-\mu), with the Landau critical exponent \mu = 1/3, the same as found for the mean-field critical behavior with respect to the source field in ferromagnets and ferroelectrics. Here reported hidden criticality of multi-band superconductors can be experimentally observed by, e.g., imaging of the variations of the vortex core in a broader temperature range. Similar effects are expected for the superconducting multilayers.Comment: 6 pages, 2 figures, Supplementary material included. Accepted for publication in PR

On the theory of pseudogap anisotropy in the cuprate superconductors

We show by means of the theory of the order parameter phase fluctuations that the temperature of "closing" (or "opening") of the gap (and pseudogap) in the electron spectra of superconductors with anisotropic order parameter takes place within a finite temperature range. Every Fourier-component of the order parameter has its own critical temperature

Fluctuations, Higher Order Anharmonicities, and Landau Expansion for Barium Titanate

Correct phenomenological description of ferroelectric phase transitions in barium titanate requires accounting for eighth-order terms in the free energy expansion, in addition to the conventional sixth-order contributions. Another unusual feature of BaTiO_3 crystal is that the coefficients B_1 and B_2 of the terms P_x^4 and P_x^2*P_y^2 in the Landau expansion depend on the temperature. It is shown that the temperature dependence of B_1 and B_2 may be caused by thermal fluctuations of the polarization, provided the fourth-order anharmonicity is anomalously small, i. e. the nonlinearity of P^4 type and higher-order ones play comparable roles. Non-singular (non-critical) fluctuation contributions to B_1 and B_2 are calculated in the first approximation in sixth-order and eighth-order anharmonic constants. Both contributions increase with the temperature, which is in agreement with available experimental data. Moreover, the theory makes it possible to estimate, without any additional assumptions, the ratio of fluctuation (temperature dependent) contributions to coefficients B_1 and B_2. Theoretical value of B_1/B_2 appears to be close to that given by experiments.Comment: 5 pages, 1 figur