Phase transition for Ising frustration potentials

A frustration potential is a sum of interactions the terms of which are not simultaneously minimized even in the ground-state spin configurations. Ising models with such potentials can be discussed by the use of contours. The Peierls condition for the phase transition can be properly generalized, taking into account the presence of zero-energy contours. Frustration has some special features in two dimensions, which we study in detail. The connection with models of spin-glasses is discussed.     

Peierls-like transition induced by frustration in a two-dimensional antiferromagnet

We show that the introduction of frustration into the spin- 1/2 two-dimensional (2D) antiferromagnetic Heisenberg model on a square lattice via a next-nearest-neighbor exchange interaction can lead to a Peierls-like transition, from a tetragonal to an orthorhombic phase, when the spins are coupled to adiabatic phonons. The two different orthorhombic ground states define an Ising order parameter, which is expected to lead to a finite temperature transition. Implications for Li(2)VOSiO(4), the first realization of that model, will be discussed.     

Conductance distribution near the Anderson transition

Using a modification of the Shapiro approach, we introduce the two-parameter family of conductance distributions W(g), defined by simple differential equations, which are in the one-to-one correspondence with conductance distributions for quasi-one-dimensional systems of size L ^d–1 × L _z , characterizing by parameters L/ξ and L _z /L (ξ is the correlation length, d is the dimension of space). This family contains the Gaussian and log-normal distributions, typical for the metallic and localized phases. For a certain choice of parameters, we reproduce the results for the cumulants of conductance in the space dimension d = 2 + ? obtained in the framework of the σ-model approach. The universal property of distributions is existence of two asymptotic regimes, log-normal for small g and exponential for large g. In the metallic phase they refer to remote tails, in the critical region they determine practically all distribution, in the localized phase the former asymptotics forces out the latter. A singularity at g = 1, discovered in numerical experiments, is admissible in the framework of their calculational scheme, but related with a deficient definition of conductance. Apart of this singularity, the critical distribution for d = 3 is well described by the present theory. One-parameter scaling for the whole distribution takes place under condition, that two independent parameters characterizing this distribution are functions of the ratio L/ξ.     

Effect of frustration on the magnetization in nickel ferrite-chromites

A study is reported on the behavior of the isotherms of the magnetization σ(H) and of the longitudinal λ_‖(H), transverse λ_⊥(H), volume ω(H), and anisotropic λ_t(H) magnetostrictions measured at T=80 K in the Cu_0.4Fe_0.6[Ni_0.6Cr_1.4]O₄ and Zn_0.4Fe_0.6[Ni_0.6Cr_1.4]O₄ ferrite-chromites having a frustrated magnetic structure. It has been established that these ferrite-chromites do not undergo technical magnetization and that the growth of the magnetization with the field is accounted for by two paraprocesses of different natures.     

Director dynamics near the nematic-smectic-A phase transition

The Landau-de Gennes model for the free energy of a nematic liquid crystal near the phase transition to the smectic A-phase is used to determine the frequency dependence of the fluctuation corrections to the Frank elastic constants. It is shown that the interaction of the fluctuations of the smectic order parameter and the director results in corrections to all the Frank elastic constants. In the low-frequency limit (ω→0), the corrections to the Frank elastic constants K ₂₂ and K ₃₃ are the largest, and decrease to zero in the infinite-frequency limit. The correction to K ₁₁ is negative, and vanishes in both limits. The absolute value of the correction to K ₁₁ is the largest at frequencies in the megahertz range. It is shown that in oriented nematics the interaction of the smectic fluctuations and the director limits deviations of the director from the direction of preferred orientation, as a result of which relaxation of both inhomogeneous and homogeneous distortions of the director field can be observed. It is also shown that this gives rise to a frequency interval in the megahertz range in which shear waves begin to propagate in the nematic. The propagation speed of these waves is roughly a hundred times smaller than that of sound and strongly depends on the direction of propagation. Zh. éksp. Teor. Fiz. 114, 2022–2033 (December 1998)     

Quantum critical transport near the Mott transition

We perform a systematic study of incoherent transport in the high temperature crossover region of the half filled one-band Hubbard model. We demonstrate that the family of resistivity curves displays characteristic quantum critical scaling of the form ρ(T, δU) = ρ(c)(T)f(T/T?(δU)), with T?(δU) ~ |δU|(zν), and ρ(c)(T) ~ T. The corresponding β function displays a "strong coupling" form β ~ ln(ρ(c)/ρ), reflecting the peculiar mirror symmetry of the scaling curves. This behavior, which is surprisingly similar to some experimental findings, indicates that Mott quantum criticality may be acting as the fundamental mechanism behind the unusual transport phenomena in many systems near the metal-insulator transition.     

Coherent backscattering near the two-dimensional metal-insulator transition

We have studied corrections to conductivity due to the coherent backscattering in low-disordered two-dimensional electron systems in silicon for a range of electron densities including the vicinity of the metal-insulator transition, where the dramatic increase of the spin susceptibility has been observed earlier. We show that the corrections, which exist deeper in the metallic phase, weaken upon approaching the transition and practically vanish at the critical density, thus suggesting that the localization is suppressed near and at the transition even in zero field.     

Step-by-step first order antiferroelectric-paraelectric transition induced by frustration and electric field

We show analytically that even not too strong frustrating next neighbor interaction strongly affects first order antiferroelectric-paraelectric transition in an external electric field. We apply mean-field Landau theory. In the electric field a single phase transition at T ₀ splits into a step-by-step staircase with a series of intermediate phases. Unexpectedly enough we found that the equilibrium structures of the phases differ substantially from structures formed at low temperature both without field and in field. Polarization of intermediate structures decreases with temperature in a stepwise manner. Similar step-by-step transitions can occur also in magnetic materials with frustrating interaction.     

Nonlinear optics near the metal insulator transition

Large, free-carrier-induced, optical nonlinearities are observed in n-Si:P near the metal-insulator transition. _X⁽³⁾ varies superlinearly with n, suggesting an impurity interaction mechanism. A theory of the effect shows that it measures the pile-up of electron density at the impurities. The experiments imply that the pile-up varies rapidly with electron energy near the transition.     

Relaxation near transition metal surfaces

A simple calculation of the relaxation near transition metal surfaces is described. The d electrons are treated in a tight-binding approximation and Born-Mayer type potentials are used to simulate the repulsive part of the energy at short distances. The interplanar spacing is found to decrease at the center of the series and to increase on the wings. For almost empty or filled bands one obtains no relaxation.     

Self-diffusion of tris-naphthylbenzene near the glass transition temperature

We present a direct measurement of self-diffusion of a single-component glass-forming liquid at the glass transition temperature. Forward recoil spectrometry is used to measure the concentration profiles of deuterio and protio 1,3-bis-(1-naphthyl)-5-(2-naphthyl)benzene (TNB) following annealing-induced diffusion in a vapor-deposited bilayer. These experiments extend the range of measured diffusion coefficients in TNB by 6 orders of magnitude. The results indicate a decoupling of translational diffusion coefficients from viscosity or rotation. At T(g), D(T) is 400 times larger than expected from the Stokes-Einstein equation.     

The effects of grain shape and frustration in a granular column near jamming

We investigate the full phase diagram of a column of grains near jamming, as a function of varying levels of frustration. Frustration is modelled by the effect of two opposing fields on a grain, due respectively to grains above and below it. The resulting four dynamical regimes (ballistic, logarithmic, activated and glassy) are characterised by means of the jamming time of zero-temperature dynamics, and of the statistics of attractors reached by the latter. Shape effects are most pronounced in the cases of strong and weak frustration, and essentially disappear around a mean-field point.     

Temperature dependence of viscosity near the glass transition

Real glass transitions, where activated processes are included, are analysed near Whitney fold and cusp singularities. In particular the temperature dependence of the viscosity is studied. For sufficiently strongly coupled systems there is close to a fold singularity located atT=T _c , a crossover from an algebraic divergence (T–T _c )^– forT>T _c , to an Arrhenius dependence exp(E/k _B T) forT<T _c . If a parameter vector specifying the system also passes close to a cusp singularity, atT ₀<T _c , there may be a temperature region where the viscosity also shows Fogel-Fulcher like dependence. The results for the viscosity are intimately connected with the dynamics for the so-called -relaxation process, where relaxation occurs via a fractal time process in the delevant time region.     

Crystal shape near the faceting phase transition point

The critical behavior of an equilibrium shape of a crystal with the size much larger than the capillary length is studied near the faceting phase transition point.