Emergence of Long-range Correlations and Rigidity at the Dynamic Glass Transition

At the microscopic level, equilibrium liquid's translational symmetry is spontaneously broken at the so-called dynamic glass transition predicted by the mean-field replica approach. We show that this fact implies the emergence of Goldstone modes and long-range density correlations. We derive and evaluate a new statistical mechanical expression for the glass shear modulus.Comment: 4 page

Critical Decay at Higher-Order Glass-Transition Singularities

Within the mode-coupling theory for the evolution of structural relaxation in glass-forming systems, it is shown that the correlation functions for density fluctuations for states at A_3- and A_4-glass-transition singularities can be presented as an asymptotic series in increasing inverse powers of the logarithm of the time t: $\phi(t)-f\propto \sum_i g_i(x)$, where $g_n(x)=p_n(\ln x)/x^n$ with p_n denoting some polynomial and x=ln (t/t_0). The results are demonstrated for schematic models describing the system by solely one or two correlators and also for a colloid model with a square-well-interaction potential.Comment: 26 pages, 7 figures, Proceedings of "Structural Arrest Transitions in Colloidal Systems with Short-Range Attractions", Messina, Italy, December 2003 (submitted

Asymptotic analysis of mode-coupling theory of active nonlinear microrheology

We discuss a schematic model of mode-coupling theory for force-driven active nonlinear microrheology, where a single probe particle is pulled by a constant external force through a dense host medium. The model exhibits both a glass transition for the host, and a force-induced delocalization transition, where an initially localized probe inside the glassy host attains a nonvanishing steady-state velocity by locally melting the glass. Asymptotic expressions for the transient density correlation functions of the schematic model are derived, valid close to the transition points. There appear several nontrivial time scales relevant for the decay laws of the correlators. For the nonlinear friction coeffcient of the probe, the asymptotic expressions cause various regimes of power-law variation with the external force, and two-parameter scaling laws.Comment: 17 pages, 12 figure

Thermodynamics of the two-dimensional frustrated J1-J2 Heisenberg ferromagnet in the collinear stripe regime: Susceptibility and correlation length

We calculate the temperature dependence of the correlation length xi and the uniform susceptibility chi_0 of the frustrated J1-J2 square-lattice Heisenberg ferromagnet in the collinear stripe phase using Green-function technique. The height chi_{max} and the position T(chi_{max}) of the maximum in the chi_0(T) curve exhibit a characteristic dependence on the frustration parameter J2/|J1|, which is well described by power laws, chi_{max}=a(J2-J2^c)^{-nu} and T(chi_{max})=b(J_2-J_2^c), where J2^c = 0.4 and nu is of the order of unity.The correlation length diverges at low temperatures as xi \propto e^{A/T}, where A increases with growing J2/|J1|. We also compare our results with recent measurements on layered vanadium phosphates and find reasonable agreement.Comment: 7 pages, 5 figures, version as published in Phys. Rev.

Self-diffusion in sheared colloidal suspensions: violation of fluctuation-dissipation relation

Using memory-function formalism we show that in sheared colloidal suspensions the fluctuation-dissipation theorem for self-diffusion, i.e. Einstein's relation between self-diffusion and mobility tensors, is violated and propose a new way to measure this violation in Brownian Dynamics simulations. We derive mode-coupling expressions for the tagged particle friction tensor and for an effective, shear-rate dependent temperature

Fragile to strong crossover coupled to liquid-liquid transition in hydrophobic solutions

Using discrete molecular dynamics simulations we study the relation between the thermodynamic and diffusive behaviors of a primitive model of aqueous solutions of hydrophobic solutes consisting of hard spheres in the Jagla particles solvent, close to the liquid-liquid critical point of the solvent. We find that the fragile-to-strong dynamic transition in the diffusive behavior is always coupled to the low-density/high-density liquid transition. Above the liquid-liquid critical pressure, the diffusivity crossover occurs at the Widom line, the line along which the thermodynamic response functions show maxima. Below the liquid-liquid critical pressure, the diffusivity crossover occurs when the limit of mechanical stability lines are crossed, as indicated by the hysteresis observed when going from high to low temperature and vice versa. These findings show that the strong connection between dynamics and thermodynamics found in bulk water persists in hydrophobic solutions for concentrations from low to moderate, indicating that experiments measuring the relaxation time in aqueous solutions represent a viable route for solving the open questions in the field of supercooled water.Comment: 6 pages, 4 figures. Accepted for publication on Physical Review

The magnetization process of the spin-one triangular-lattice Heisenberg antiferromagnet

We apply the coupled cluster method and exact diagonalzation to study the uniform susceptibility and the ground-state magnetization curve of the triangular-lattice spin-1 Heisenberg antiferromagnet. Comparing our theoretical data for the magnetization curve with recent measurements on the s=1 triangular lattice antiferromagnet Ba3NiSb2O9 we find a very good agreement.Comment: 2 pages, 3 figure

Tests of mode coupling theory in a simple model for two-component miscible polymer blends

We present molecular dynamics simulations on the structural relaxation of a simple bead-spring model for polymer blends. The introduction of a different monomer size induces a large time scale separation for the dynamics of the two components. Simulation results for a large set of observables probing density correlations, Rouse modes, and orientations of bond and chain end-to-end vectors, are analyzed within the framework of the Mode Coupling Theory (MCT). An unusually large value of the exponent parameter is obtained. This feature suggests the possibility of an underlying higher-order MCT scenario for dynamic arrest.Comment: Revised version. Additional figures and citation