Inverse transitions in the Ghatak–Sherrington model with bimodal random fields

The present work studies the Ghatak–Sherrington (GS) model in the presence of a longitudinal magnetic random field (RF) _hi$h_i$ following a bimodal distribution. The model considers a random bond interaction _Ji,j$J_{i,j}$ which follows a Gaussian distribution with mean _J0/N$J_0/N$ and variance J²/N$J^2/N$. This allows us to introduce the bond disorder strength parameter J/_J0$J/J_0$ to probe the combined effects of disorder coming from the random bond and the discrete RF over unusual phase transitions known as inverse transitions (ITs). The results within a mean field approximation indicate that these two types of disorder have completely distinct roles for the ITs. They indicate that bond disorder creates the necessary conditions for the presence of inverse freezing, or even inverse melting, depending on the bond disorder strength, while the RF tends to enforce mechanisms that destroy the ITs.     

Linear entropy dynamics of the field in the Jaynes－Cummings model with an intensity-dependent coupling in the dispersive approximation

We present the linear entropy dynamics of the field state in the dispersive cavity in the Jaynes－Cummings model with an intensity-dependent coupling in the dispersive approximation, and investigate the influence of dissipation on entanglement between the field and the atoms. We show that the coherence properties of the field are also affected by the cavity when the nonlinear process of the field interacting with the atoms with an intensity-dependent coupling is involved, and find that the dissipation constant, the intensity of the field and the atomic distribution angle have different influence on the coherence properties of the field.     

Critical dynamics of the sine-Gordon model ind=2−ε dimensions

The renormalization scheme of Amit, Goldschmidt and Grinstein is extended tod=2?ε dimensions. The exponent ν of the correlation lengthv ^?1=2ε+O(ε²) is in agreement with the result of Kosterlitz for the Coulomb gas. The exponent η of the correlation function of the sine-Gordon field is η=ε+O(ε²). The scaling form of the dynamical structure factorS(q,ω) of the dynamic sine-Gordon ModelA is studied ind=2?ε dimensions. The dynamic exponentz is found to bez=2+(b?1)ε+O(ε²) for ε≧0. The constantb is given by the integral $$b = \int\limits_0^\infty {dss^{ - 2} \exp } \left( { - 2\int\limits_s^\infty {dxx^{ - 1} e^{ - x} } } \right) = 2,371544...$$      

The multielectron dissociative ionization dynamics of N2 molecule in intense femtosecond laser fields with arbitrary polarization

The field-ionization Coulomb explosion model is extended to investigate the multielectron dissociative ionization process of N₂ molecule irradiated by an intense femtosecond laser field with an arbitrary polarization. The ionization process of N₂ molecule is found to be optimal at the critical internuclear distance R_c=7a.u., which is independent of the laser polarization state, the molecular explosion channel and the angle between the molecular axis and the direction of laser electric field. The kinetic energies of the ion fragments are identical in the cases of linear and circular polarizations at the same incident laser intensity. However,the probability of electron ionization is very sensitive to the above three parameters. At the critical distance R_c=7a.u. the angular dependence of the threshold intensity for the over-the-barrier ionization leads to the geometric alignment of molecules in the case of linear polarization. The threshold intensity in the case of circular polarization is apparently higher than that in the case of linear polarization, which can well explain the significant decrease of ionization in the case of circular polarization. The numerical calculations are compared with the experimental measurements.     

‘1001’ correlations in random wave fields

Abstract

Correlations in Gaussian speckle patterns are discussed for the intensity and the phase, as well as for the real and imaginary parts of the wavefunction. Application of the sampling theorem to the wave field is described, and five topologically mandated deterministic rules are enumerated that constrain many aspects of the field structure. A brief overview is given of wave-field correlation matrices containing several million coefficients.     

Effect of random magnetic fields on the hyperfine structure of Mössbauer spectra in paramagnetic single crystals

Under certain conditions, the⁵⁷Fe Mössbauer spectra of Al(NO₃)₃·9H₂OFe³⁺ single crystals exhibit new lines [1,2] (so-called z-lines) at an unusually high velocity of about 10.5 mm/s. The dependence of the positions and intensities of these z-lines on the magnitude and direction of an external magnetic field has been investigated. The appearance of the z-lines is explained by small random magnetic fields arising from magnetic nuclei in the crystal.     

Depinning dynamics of driven colloids with random pinning： a numerical study

Using Langevin simulations, we have investigated numerically the depinning dynamics of driven two-dimensional colloids subject to the randomly distributed point-like pinning centres. With increasing strength of pinning, we find a crossover from elastic to plastic depinnings, accompanied by an order to disorder transition of state and a substantial increase in the depinning force. In the elastic regime, no peaks are found in the differential curves of the velocity－force dependence (VFD) and the transverse motion is almost none. In addition, the scaling relationship between velocity and force is found to be valid above depinning. However, when one enters the plastic regime, a peak appears in the differential curves of VFD and transverse diffusion occurs above depinning. Furthermore, history dependence is found in the plastic regime.     

Critical exponentβ for hyperfine fields in nickel

The magnetic hyperfine fields for⁶³Ni,⁶⁶Cu, and⁶⁷Zn nuclei in nickel metal have been measured by means of perturbed-ray angular distribution techniques at different temperatures up to 1 K below the Curie temperature,T _C . The temperature dependence of the fields can be very well fitted by (1—T/T _C ) with best values=0.322(16) for⁶³NiNi, = 0.427(42) for⁶⁶CuNi, and=0.427(14) for⁶⁷ZnNi respectively. The differences between these exponents indicate that there could be probe atom dependent deviations from proportionality between hyperfine field and bulk magnetization in the critical region.Work performed in partial fulfillment of the requirements for a doctorate in physics at the Freie Universität, Berlin     

Localization in the ground-state of the one dimensionalX−Y model with a random transverse field

We consider the ground-state of the quantum spin model in one-dimension, where {h _i, iZ} are independent identically distributed random variables. By means of a Jordan-Wigner transformation the model is mapped into a free Fermi gas in the presence of a random external potential. We then use exponential localization of the one particle states to prove exponential decay for the spin-spin correlation functions.Partially supported by the NSF under grants DMS8702301 and INT8703059Partially supported by the CNPq under grant 303795-77FA     

Metastability of Ising spin chains with nearest—neighbour and next—nearest—neighbour interactions in random fields

One-dimensional Ising systems in random fields (RFs) are studied taking into account the nearest-neighbour and next-nearest-neighbour interactions. We investigate two distributions of RFs: binary and Gaussian distributions. We consider four cases of the exchange couplings: ferro－ferromagnetic (F－F), ferro－antiferromagnetic (F－AF), antiferro－ferromagnetic (AF－F) and antiferro－antiferromagnetic (AF－AF). The energy minima of chains of no more than 30 spins with periodic boundary conditions are analysed exactly. We found that the average number of energy minima grows exponentially with the number of spins in both cases of RFs. The energy distributions across the corresponding energy minima are shown. The effects of RFs on both the average and density of metastable states are explained. For a weak RF, the energy distributions display a multipartitioned structure. We also discuss the frustration effect due to RFs and exchange fields. Finally, the distributions of magnetization are calculated. The absolute value of magnetization averaged over all metastable states decreases logarithmically with the number of spins.     

2D Pauli Equation with Hulthén Potential in the Presence of Aharonov-Bohm Effect

The 2D Pauli equation with Hulthén potential for spin-1/2 particle in the presence of Aharonov-Bohm (AB) field is solved analytically, on the assumption that an effective approximation is used for the centrifugal term.Singular and regular solutions of the problem are obtained. It is shown that the AB field lifts the degeneracy of the energy levels. The range of the flux parameter for which singular solutions are allowed is modified compared to the pure AB case. When the screening parameter vanishes, it is shown that the obtained energy spectrum becomes the same as that of the Aharonov-Bohm Coulomb problem.     

The effects of random fields on the critical and bicritical behavior of Mn x Zn1−x F2

We have carried out a comprehensive study of the static and dynamic spin-spin correlations of Mn _x Zn_1–x F₂ in a magnetic field. Samples withx=0.75 andx=0.5 have been studied. This system exhibits behavior closely related, if not identical, to that of the Random Field Ising Model (RFIM). An additional feature of Mn _x Zn_1–x F₂ is that it exhibits an easily accessible bicritical point; thus one can study the changeover from the RFIM to the uniformXY model with a transverse random field. Quite generally, the instantaneous spin-spin correlations in a field are described by a combination of Lorentzian, Lorentzian-squared and delta function terms the latter corresponds to the long range order (LRO) component. In the Ising phase one finds history dependent behavior as discussed previously. In theXY phase, except very near the spin-flop boundary, one finds ergodic behavior withXY LRO and Lorentzian squared Ising fluctuations. Rather complicated instability effects are found all along the spin-flop boundary. Further, when one establishes LRO in theXY phase and lowers the field through the spin-flop value, one obtains a LRO Ising state in thex=0.75 sample whereas one obtains the field-cooled domain state in thex=0.50 sample. This dramatic difference in behavior is not understood. Our results on the RFIM aspects of the problem are consistent with our previous studies. The transition is dominated by the metastability effects with an underlying equilibrium transition which is either first order or weakly second order (0). The underlying transition manifests itself directly in measurements of the dynamic response nearT _N (H). From the data above the metastability boundary we deduce for the static correlation length exponentv=1.4±0.3 in good agreement with theory. We find for the RFIM crossover exponent _RF=1.5±0.2 where the errors represent the spread in values obtained from different techniques. Finally, we have determined in detail the field-temperature phase diagram of thex=0.5 sample including the critical behavior along the spin-flop line; the latter transition appears to be second order for an extended region.     

Existence of the critical point in φ4 field theory

We consider the ⁴ quantum field theory in two and three spacetime dimensions. In the single phase region the physical mass (inverse correlation length)m() decreases continuously to zero as the bare mass parameter approaches a critical value _c from above. In three dimensions the critical point _c is in the single phase region and the physical mass vanishes there,m( _c )=0.A consequence of our results is that the critical exponentv governing the approach to infinite correlations is bounded below (rigorously) by its classical value, 1/2.Supported in part by the National Science Foundation under Grant MPS74-13252     

Critical points and points of the bifurcation of the rotating magnetized newtonian polytropes with a 1 ⩽ n ⩽ 1.6 index

The presence of critical points and the bifurcation points of rotating Newtonian polytropes with an index of 1 ? n ? 1.6 has been shown for the first time in this paper. The symbolic-numerical calculation error in metric L ₂ has reached the size of the 10^?4 order. The approximate analytical solution to the problem to the abovementioned accuracy has been set forth. A critical value of the polytropes index n = n _k = 1.51025 has been calculated which is the highest among the critical points and bifurcation points. The value n _k corresponds to the infinitely slow polytropes rotation. Furthermore, in this paper the presence of the period jump at the bifurcation point T _b has been predicted and the relative value of this jump ΔT _b /T _b ～ B _0in ^4/3 has been estimated.     

Beyond the Monchick–Mason approximation: the mobility of Li+ Ions in H2

The Monchick–Mason approximation for the calculation of the transport coefficients of atomic ions in diatomic gases is extended in a manner that allows comparison of theoretical and experimental mobilities of gaseous ions to serve as quantitative tests of the accuracy of the ab initio, angle- and position-dependent interaction potentials used in the calculations. The feasibility of this procedure is demonstrated with Li⁺ in H₂.