174 research outputs found
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, , are derived in the framework of the suggested approach.Comment: 4 pages, 4 figures; Added references; correction
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 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 for arbitrary
temperatures. We carefully extrapolate our numerical results to the critical
point and determine the order parameter exponent , in
reasonable agreement with the expected value 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
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
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() model and interacting bosons at zero temperature, using a variety of
techniques: perturbation theory, hydrodynamic approach (i.e., for bosons,
Popov's theory), large- limit and non-perturbative renormalization group. We
emphasize the essential role of the Ginzburg momentum scale 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()
model and interacting bosons at zero temperature.Comment: v2) 19 pages, 8 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
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
Viscosity and thermal conductivity effects at first-order phase transitions in heavy-ion collisions
Effects of viscosity and thermal conductivity on the dynamics of first-order
phase transitions are studied. The nuclear gas-liquid and hadron-quark
transitions in heavy-ion collisions are considered. We demonstrate that at
non-zero thermal conductivity, , onset of spinodal instabilities
occurs on an isothermal spinodal line, whereas for instabilities
take place at lower temperatures, on an adiabatic spinodal.Comment: invited talk at 6th International Workshop on Critical Point and
Onset of Deconfinment (CPOD2010), Dubna, August 22-28, 201
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
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