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

Paraelectric in a Strong High-Frequency Field

A change in the effective permittivity of a ferroelectric film in the paraelectric phase under the action of a strong high-frequency field (nonequilibrium soft mode heating) is considered. It is shown that this effect must be most clearly pronounced far from the resonance (\omega_0 << \omega_sm), rather than for the external field frequency \omega_0 close to the soft mode frequency \omega_sm. The effective permittivity as a function of the high-frequency field amplitude is calculated using the phenomenological approach and within the microscopic theory based on the simple model of a displacement-type ferroelectric.Comment: 3 two-column page

Pseudo-epsilon expansion and the two-dimensional Ising model

Starting from the five-loop renormalization-group expansions for the two-dimensional Euclidean scalar \phi^4 field theory (field-theoretical version of two-dimensional Ising model), pseudo-\epsilon expansions for the Wilson fixed point coordinate g*, critical exponents, and the sextic effective coupling constant g_6 are obtained. Pseudo-\epsilon expansions for g*, inverse susceptibility exponent \gamma, and g_6 are found to possess a remarkable property - higher-order terms in these expansions turn out to be so small that accurate enough numerical estimates can be obtained using simple Pade approximants, i. e. without addressing resummation procedures based upon the Borel transformation.Comment: 4 pages, 4 tables, few misprints avoide

Polarization of the fermionic vacuum by a global monopole with finite core

We study the vacuum polarization effects associated with a massive fermionic field in a spacetime produced by a global monopole considering a nontrivial inner structure for it. In the general case of the spherically symmetric static core with finite support we evaluate the vacuum expectation values of the energy-momentum tensor and the fermionic condensate in the region outside the core. These quantities are presented as the sum of point-like global monopole and core-induced contributions. The asymptotic behavior of the core-induced vacuum densities are investigated at large distances from the core, near the core and for small values of the solid angle corresponding to strong gravitational fields. As an application of general results the flower-pot model for the monopole's core is considered and the expectation values inside the core are evaluated.Comment: 22 pages, 4 figure

Anharmonicity of BaTiO_3 single crystals

By analyzing the dielectric non-linearity with the Landau thermodynamic expansion, we find a simple and direct way to assess the importance of the eighth order term. Following this approach, it is demonstrated that the eighth order term is essential for the adequate description of the para/ferroelectric phase transition of BaTiO_3. The temperature dependence of the quartic coefficient \beta is accordingly reconsidered and is strongly evidenced by the change of its sign above 165 C. All these findings attest to the strong polarization anharmonicity of this material, which is unexpected for classical displacive ferroelectrics.Comment: 4 figures, to be published in Phys. Rev.

Constraints On The Topology Of The Universe From The WMAP First-Year Sky Maps

We compute the covariance expected between the spherical harmonic coefficients $a_{\ell m}$ of the cosmic microwave temperature anisotropy if the universe had a compact topology. For fundamental cell size smaller than the distance to the decoupling surface, off-diagonal components carry more information than the diagonal components (the power spectrum). We use a maximum likelihood analysis to compare the Wilkinson Microwave Anisotropy Probe first-year data to models with a cubic topology. The data are compatible with finite flat topologies with fundamental domain $L > 1.2$ times the distance to the decoupling surface at 95% confidence. The WMAP data show reduced power at the quadrupole and octopole, but do not show the correlations expected for a compact topology and are indistinguishable from infinite models.Comment: 16 pages, 5 figure