Large-Order Behavior of Two-coupling Constant ϕ4\phi^4-Theory with Cubic Anisotropy

For the anisotropic [u (\sum_{i=1^N {\phi}_i^2)^2+v \sum_{i=1^N \phi_i^4]-theory with {$N=2,3$} we calculate the imaginary parts of the renormalization-group functions in the form of a series expansion in $v$, i.e., around the isotropic case. Dimensional regularization is used to evaluate the fluctuation determinants for the isotropic instanton near the space dimension 4. The vertex functions in the presence of instantons are renormalized with the help of a nonperturbative procedure introduced for the simple g{\phi^4-theory by McKane et al.Comment: LaTeX file with eps files in src. See also http://www.physik.fu-berlin.de/~kleinert/institution.htm

Critical Behavior of an Ising System on the Sierpinski Carpet: A Short-Time Dynamics Study

The short-time dynamic evolution of an Ising model embedded in an infinitely ramified fractal structure with noninteger Hausdorff dimension was studied using Monte Carlo simulations. Completely ordered and disordered spin configurations were used as initial states for the dynamic simulations. In both cases, the evolution of the physical observables follows a power-law behavior. Based on this fact, the complete set of critical exponents characteristic of a second-order phase transition was evaluated. Also, the dynamic exponent $\theta$ of the critical initial increase in magnetization, as well as the critical temperature, were computed. The exponent $\theta$ exhibits a weak dependence on the initial (small) magnetization. On the other hand, the dynamic exponent $z$ shows a systematic decrease when the segmentation step is increased, i.e., when the system size becomes larger. Our results suggest that the effective noninteger dimension for the second-order phase transition is noticeably smaller than the Hausdorff dimension. Even when the behavior of the magnetization (in the case of the ordered initial state) and the autocorrelation (in the case of the disordered initial state) with time are very well fitted by power laws, the precision of our simulations allows us to detect the presence of a soft oscillation of the same type in both magnitudes that we attribute to the topological details of the generating cell at any scale.Comment: 10 figures, 4 tables and 14 page

New approach to Borel summation of divergent series and critical exponent estimates for an N-vector cubic model in three dimensions from five-loop \epsilon expansions

A new approach to summation of divergent field-theoretical series is suggested. It is based on the Borel transformation combined with a conformal mapping and does not imply the exact asymptotic parameters to be known. The method is tested on functions expanded in their asymptotic power series. It is applied to estimating the critical exponent values for an N-vector field model, describing magnetic and structural phase transitions in cubic and tetragonal crystals, from five-loop \epsilon expansions.Comment: 9 pages, LaTeX, 3 PostScript figure

The Magnetization of the 3D Ising Model

We present highly accurate Monte Carlo results for simple cubic Ising lattices containing up to $256^3$ spins. These results were obtained by means of the Cluster Processor, a newly built special-purpose computer for the Wolff cluster simulation of the 3D Ising model. We find that the magnetization $M(t)$ is perfectly described by $M(t)=(a_0-a_1 t^{\theta} - a_2 t) t^{\beta}$, where $t=(T_{\rm c}-T)/T_{\rm c}$, in a wide temperature range $0.0005 < t < 0.26$. If there exist corrections to scaling with higher powers of $t$, they are very small. The magnetization exponent is determined as $\beta=0.3269$ (6). An analysis of the magnetization distribution near criticality yields a new determination of the critical point: $K_{\rm c}=J/k_B T_{\rm c}=0.2216544$, with a standard deviation of $3\cdot 10^{-7}$.Comment: 7 pages, 5 Postscript figure

Coupled valence and spin state transition in (Pr0.7Sm0.3)0.7Ca0.3CoO3

The coupled valence and spin state transition (VSST) taking place in (Pr0.7Sm0.3)0.7Ca0.3CoO3 was investigated by soft x-ray absorption spectroscopy (XAS) experiments carried out at the Pr-M4,5, Co-L2,3, and O-1s edges. This VSST is found to be composed of a sharp Pr/Co valence and Co spin state transition centered at T*=89.3 K, followed by a smoother Co spin-state evolution at higher temperatures. At T < T*, we found that the praseodymium displays a mixed valence Pr3+/Pr4+ with about 0.13 Pr4+/f.u., while all the Co3+ is in the low-spin (LS) state. At T around T*, the sharp valence transition converts all the Pr4+ to Pr3+ with a corresponding Co3+ to Co4+ compensation. This is accompanied by an equally sharp spin state transition of the Co3+ from the low to an incoherent mixture of low and high spin (HS) states. An involvement of the intermediate spin (IS) state can be discarded for the Co3+. While above T* and at high temperatures the system shares rather similar properties as Sr-doped LaCoO3, at low temperatures it behaves much more like EuCoO3 with its highly stable LS configuration for the Co3+. Apparently, the mechanism responsible for the formation of Pr4+ at low temperatures also helps to stabilize the Co3+ in the LS configuration despite the presence of Co4+ ions. We also found out that that the Co4+ is in an IS state over the entire temperature range investigated in this study (10-290 K). The presence of Co3+ HS and Co4+ IS at elevated temperatures facilitates the conductivity of the material.Comment: 19 pages, 7 figures, Accepted in PR

Topological and Universal Aspects of Bosonized Interacting Fermionic Systems in (2+1)d

General results on the structure of the bosonization of fermionic systems in $(2+1)$d are obtained. In particular, the universal character of the bosonized topological current is established and applied to generic fermionic current interactions. The final form of the bosonized action is shown to be given by the sum of two terms. The first one corresponds to the bosonization of the free fermionic action and turns out to be cast in the form of a pure Chern-Simons term, up to a suitable nonlinear field redefinition. We show that the second term, following from the bosonization of the interactions, can be obtained by simply replacing the fermionic current by the corresponding bosonized expression.Comment: 29 pages, RevTe

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

Short-time Critical Dynamics of the 3-Dimensional Ising Model

Comprehensive Monte Carlo simulations of the short-time dynamic behaviour are reported for the three-dimensional Ising model at criticality. Besides the exponent $\theta$ of the critical initial increase and the dynamic exponent $z$, the static critical exponents $\nu$ and $\beta$ as well as the critical temperature are determined from the power-law scaling behaviour of observables at the beginning of the time evolution. States of very high temperature as well as of zero temperature are used as initial states for the simulations.Comment: 8 pages with 7 figure

Critical exponents for 3D O(n)-symmetric model with n > 3

Critical exponents for the 3D O(n)-symmetric model with n > 3 are estimated on the base of six-loop renormalization-group (RG) expansions. A simple Pade-Borel technique is used for the resummation of the RG series and the Pade approximants [L/1] are shown to give rather good numerical results for all calculated quantities. For large n, the fixed point location g_c and the critical exponents are also determined directly from six-loop expansions without addressing the resummation procedure. An analysis of the numbers obtained shows that resummation becomes unnecessary when n exceeds 28 provided an accuracy of about 0.01 is adopted as satisfactory for g_c and critical exponents. Further, results of the calculations performed are used to estimate the numerical accuracy of the 1/n-expansion. The same value n = 28 is shown to play the role of the lower boundary of the domain where this approximation provides high-precision estimates for the critical exponents.Comment: 10 pages, TeX, no figure

The DICE calibration project: design, characterization, and first results

We describe the design, operation, and first results of a photometric calibration project, called DICE (Direct Illumination Calibration Experiment), aiming at achieving precise instrumental calibration of optical telescopes. The heart of DICE is an illumination device composed of 24 narrow-spectrum, high-intensity, light-emitting diodes (LED) chosen to cover the ultraviolet-to-near-infrared spectral range. It implements a point-like source placed at a finite distance from the telescope entrance pupil, yielding a flat field illumination that covers the entire field of view of the imager. The purpose of this system is to perform a lightweight routine monitoring of the imager passbands with a precision better than 5 per-mil on the relative passband normalisations and about 3{\AA} on the filter cutoff positions. The light source is calibrated on a spectrophotometric bench. As our fundamental metrology standard, we use a photodiode calibrated at NIST. The radiant intensity of each beam is mapped, and spectra are measured for each LED. All measurements are conducted at temperatures ranging from 0{\deg}C to 25{\deg}C in order to study the temperature dependence of the system. The photometric and spectroscopic measurements are combined into a model that predicts the spectral intensity of the source as a function of temperature. We find that the calibration beams are stable at the $10^{-4}$ level -- after taking the slight temperature dependence of the LED emission properties into account. We show that the spectral intensity of the source can be characterised with a precision of 3{\AA} in wavelength. In flux, we reach an accuracy of about 0.2-0.5% depending on how we understand the off-diagonal terms of the error budget affecting the calibration of the NIST photodiode. With a routine 60-mn calibration program, the apparatus is able to constrain the passbands at the targeted precision levels.Comment: 25 pages, 27 figures, accepted for publication in A&