arXiv subjects
Publications and source records attributed to Moshe Schwartz.
Random Ising systems on a general hierarchical lattice with both, random fields and random bonds, are considered. Rigorous inequalities between eigenvalues of the Jacobian renormalization matrix at the pure fixed point are obtained. These inequalities lead to upper bounds on the crossover exponents $\{ϕ_i\}$.
We obtain the memory kernel of the generalized Langevin equation, describing a particle interacting with longitudinal phonons in a liquid. The kernel is obtained analytically at T=0 Kelvin and numerically at T>0 Kelvin. We find that it shows some non-trivial structural features like negative correlations for some range of time separations. The system is shown to have three characteristic time scales, that control the shape of the kernel, and the transition between quadratic and linear behavior of the mean squared distance (MSD). Although the derivation of the structure in the memory kernel is obtained within a specific dynamical model, the phenomenon is shown to be quite generic.
We consider the time dependent two point function, <ϕ_q (t) ϕ_-q (0)> in non-linear stochastic field theories, for which the KPZ equation serves as a prototype. In particular we consider the small q's and long times such that ω_q t>>1 (ω_q being the corresponding decay rate). We find that, since the generic case has ω_q \propto q^μfor small q where μ>1, the decay of the two point function is given by a streched exponential in ω_qt multiplied by a factor of t, <ϕ_q (t) ϕ_-q (0)> \propto t^{β_d}exp[-γ(ω_qt)^{1/μ}], where β_d=(d-1)/2μ, d is the dimensionality of space and γa dimensionless constant.
A self consistent field theory that describes a part of a contour loop of a random Gaussian surface as a trajectory interacting with itself is constructed. The exponent νcharacterizing the end to end distance is obtained by a Flory argument. The result is compared with different previuos derivations and is found to agree with that of Kondev and Henley over most of the range of the roughening exponent of the random surface.
We find numerically that the sample to sample fluctuation of the entropy, $ΔS$, is a tool more sensitive in distinguishing how from high temperature behaviors, than the corresponding fluctuation in the free energy. In 1+1 dimensions we find a single phase for all temperatures since $(ΔS)^{2}$ is always extensive. In 2+1 dimensions we find a behavior may look at first sight as a transition from a low temperature phase where $(ΔS)^{2}$ is extensive to a high temperature phase where it is subextensive. This is observed in spite of the relatively large system we use. The observed behavior is explained not as a phase transition but as a strong crossover behavior. We use an analytical agreement to obtain $(ΔS)^{2}$ for high temperature and find that while it is always extensive it is also extremly small and the leading extensive part decays very fast to zero as temperature is increased.
We present systematic numerical simulations for directed polymers at finite temperatures in 1+1 and 2+1 dimensions. The transverse fluctuations and free energy fluctuations tend to the strong coupling limit at any temperature in both 1+1 and 2+1 dimensions for long time t. Two different definitions for energy fluctuations at finite temperatures, which are the ensemble energy fluctuations and the internal energy fluctuations, are investigated. Apart from zero temperature, the behavior of the energy fluctuations and the free energy fluctuations for directed polymers is shown to be different. At finite temperatures, the ensemble energy fluctuations in both 1+1 and 2+1 dimensions and internal energy fluctuations in 1+1 dimensions scale as t^{1/2} where the free energy fluctuations in 1+1 dimensions and 2+1 dimensions scale as t^{1/3} and t^{0.2} respectively. As a consequence of that the specific heat in both 1+1 and 2+1 dimensions scales as t and the entropy fluctuations in 1+1 dimensions scale as t^{1/2} at any finite temperature.
In pure anisotropic or layered superconductors thermal fluctuations induce a van der Waals attraction between flux lines. This attraction together with the entropic repulsion has interesting consequences for the low field phase diagram; in particular, a first order transition from the Meissner phase to the mixed state is induced. We introduce a new variational approach that allows for the calculation of the effective free energy of the flux line lattice on the scale of the mean flux line distance, which is based on an expansion of the free energy around the regular triangular Abrikosov lattice. Using this technique, the low field phase diagram of these materials may be explored. The results of this technique are compared with a recent functional RG treatment of the same system.
We propose a new method to generate a sequence of random numbers with long-range power-law correlations that overcomes known difficulties associated with large systems. The new method presents an improvement on the commonly-used methods. We apply the algorithm to generate enhanced diffusion, isotropic and anisotropic self-affine surfaces, and isotropic and anisotropic correlated percolation.