Exactly solvable toy model for the pseudogap state

We present an exactly solvable toy model which describes the emergence of a pseudogap in an electronic system due to a fluctuating off-diagonal order parameter. In one dimension our model reduces to the fluctuating gap model (FGM) with a gap that is constrained to be of the form , where A and Q are random variables. The FGM was introduced by Lee, Rice and Anderson [Phys. Rev. Lett. 31, 462 (1973)] to study fluctuation effects in Peierls chains. We show that their perturbative results for the average density of states are exact for our toy model if we assume a Lorentzian probability distribution for Q and ignore amplitude fluctuations. More generally, choosing the probability distributions of A and Q such that the average of vanishes and its covariance is , we study the combined effect of phase and amplitude fluctuations on the low-energy properties of Peierls chains. We explicitly calculate the average density of states, the localization length, the average single-particle Green's function, and the real part of the average conductivity. In our model phase fluctuations generate delocalized states at the Fermi energy, which give rise to a finite Drude peak in the conductivity. We also find that the interplay between phase and amplitude fluctuations leads to a weak logarithmic singularity in the single-particle spectral function at the bare quasi-particle energies. In higher dimensions our model might be relevant to describe the pseudogap state in the underdoped cuprate superconductors. Received 15 March 2000     

Exactly solvable model of a spin glass

Sherrington and Kirkpatrick presented a solvable model of a spin glass. In the solution, they used a mathematically unwarranted procedure. In the present article, we show that the problem is exactly solved by starting with the virial expansion formula, and confirm the results of Sherrington and Kirkpatrick. The solution is obtained for the random Ising magnet in which the external field of each site and the exchange integral between each pair of sites are random variables. We obtain the exact thermodynamic properties for this system in the limit of n_w→∞, assuming that the exchange integrals of a spin with O(n_w) neighbours are $\text{O(n}{}_{\mathrm{w}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{)}$ and the average value of each is O(n_w^?1). The system is found to show the spin-glass state as well as the paramagnetic and the ferromagnetic state.     

Exactly solvable XY model of the spin Peierls transition

The exact solution of the problem of the ground state of theXY-spin system on a deformed chain is found. At finite magnetizationm it is characterized by the double periodic structure and has a finite-band spectrum of spin excitations. Atm 0 the phase transition from the incommensurate into the dimerized state is accompanied by the soliton lattice formation.     

Exactly solvable model of a structural phase transition

An exactly solvable d-dimensional model for the structural phase transition with long-range anharmonic interaction is considered. Classical as well as purely quantum regimes are discussed within the framework of the method of approximating Hamiltonians.     

Relaxation, crystallization, and glass transition in supercooled liquid Ni

In this Letter, molecular dynamics (MD) simulations based on EAM many-body potential have been performed to investigate the differences of dynamical heterogeneity in the course of crystallization and glass transition, respectively. The crystallization of liquid, detected at a cooling rate of , is characterized by the appearances of the second plateau in mean square displacement (MSD) and the nonzero plateau in non-Gaussian parameter (NGP). It implies that the non-diffusive rearrangement of atoms occurring at a certain temperature and relaxation time leads to nucleus forming. The glass phase forms as the cooling rate increases to . There is no second plateau in MSD appearing in the formation of metallic glass, indicating the diffusive motion of atoms. The non-Gaussian characteristic in NGP is more obvious at low temperatures.     

Dynamics of supercooled liquids and understanding the glass transition

The self-consistent mode coupling theory of glass transition is briefly reviewed. The existance of a temperature T_c, higher than the usual calorimetric glass transition temperature, across which the dynamics of the fluid becomes quite different are indicated through different experimental results. Above T_c the viscosity tends to diverge with a power law while for lower temperature this sharp transition is cutoff. Such changes in the transport properties can be understood from the self-consistent mode coupling theory. The relaxation functions predicted by the mode-coupling theory over different time scales are indicated. The models with proper wave-vector dependence are also discussed.     

Properties of the glass instability treated within a mode coupling theory

The anomalies at the liquid glass transition discussed recently by Bengtzelius et al. within a mode coupling theory are demonstrated to be due to an isolated eigenvalue of a certain stability matrix to approach unity at the critical point. Within this scenario it is shown how to derive the asymptotic results for the correlations functions analytically up to the determination of two eigenvectors and the evaluation of some wave vector integrals. As a result it is found that the Debye-Waller factor, the Lamb-Mössbauer factor, the localization length for a tagged particle, and the elastic moduli approach their asymptotic limit at the glass instability point with critical exponent one half. The critical dynamics for the coherent and incoherent scattering functions and for the transversal currents is given by a single wave vector independend scaling function. A formula for the critical exponent parameter is obtained and the scaling equation is shown to agree with the one discussed earlier for a schematic model.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Exactly solvable models of conformal-invariant quantum field theory in D-dimensional space

The method for exact solution of a certain class of models of conformal quantum field theory in D-dimensional Euclidean space is proposed. The method allows one to derive closed differential equations for all the Green functions and also algebraic equations to scale dimensions of all field. A scalar field P of a scale dimension d_p = D − 2 is needed for nontrivial solutions to exist. At D ≠ 2 this field is converted to a constant that coincides with the central charge of two-dimensional theories. A new class of D = 2 models has been obtained, where the infinite-parametric symmetry is not manifest. The two-dimensional Wess-Zumino model is used to illustrate the method of solution.     

Exactly solvable totally reducible parasupersymmetric model of a quantum oscillator

We use a sequence of N Darboux transforms for a stationary one-dimensional Schrodinger equation to construct an N-dimensional parasuperalgebra including superhamiltonians and supercharges, which are differential matrix operators with orders from one to N. We consider the harmonic oscillator as an example. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 84–87. October, 1996.     

Exactly solvable model of avalanches dynamics for Barkhausen crackling noise

We review the present state of understanding of the Barkhausen effect in soft ferromagnetic materials. Barkhausen noise (BN) is generated by the discontinuous motion of magnetic domains as they interact with impurities and defects. BN is one of the many examples of crackling noise, arising in a variety of contexts with remarkably similar features, and occurring when a system responds in a jerky manner to a smooth external forcing. Among all crackling system, we focus on BN, where a complete and consistent picture emerges thanks to an exactly solvable model of avalanche dynamics, known as the ABBM model, which ultimately describes the system in terms of a Langevin equation for the velocity of the avalanche front. Despite its simplicity, the ABBM model is able to accurately reproduce the phenomenology observed in the experiments on a large class of magnetic materials, as long as universal properties are involved. To complete the picture and to understand the long-standing discrepancy between the ABBM theory and the experiments, which otherwise agree exceptionally well, consisting of the puzzling asymmetric shape of the noise pulses, microscopic details must be taken into account, namely the effects of eddy current retardation. These effects can be incorporated in the model, and result, to a first-order approximation, in a negative effective mass associated with the wall. The progress made in understanding BN is potentially relevant for other crackling systems: on the one hand, the ABBM model turns out to be a paradigmatic model for the universal behaviour of avalanche dynamics; on the other hand, the microscopic explanation of the asymmetry in the noise pulses suggests that inertial effects may also be at the origin of pulses asymmetry observed in other crackling systems.     

Exactly solvable spin ladder model with degenerate ferromagnetic and singlet states

We study the spin ladder model with interactions between spins on neighboring rungs. The model Hamiltonian with the exact singlet ground state degenerated with ferromagnetic state is obtained. The singlet ground state wave function has a special recurrent form and depends on two parameters. Spin correlations in the singlet ground state show double-spiral structure with period of spirals equals to the system size. For special values of parameters they have exponential decay. The spectrum of the model is gapless and there are asymptotically degenerated excited states for special values of parameters in the thermodynamic limit. Received 7 May 1999     

Experimental evidence for fast heterogeneous collective structural relaxation in a supercooled liquid near the glass transition

We have extended the exploration of microscopic dynamics of supercooled liquids to small wave numbers Q corresponding to the scale of intermediate range order, by developing a new experimental approach for precise data correction for multiple scattering noise in inelastic coherent neutron scattering. Our results in supercooled Ca0.4K0.6(NO3)(1.4) reveal the first direct experimental evidence, after a decade of controversy, that the so-called picosecond process around the glass transition corresponds to a predicted first, faster stage of the structural relaxation. In addition, they show that this process takes the spatial form of fast heterogeneous collective flow of correlated groups of atoms.