Strings with Extrinsic Curvature: An Analysis of the Crossover Regime

We present the results of a set of Monte Carlo simulations of Dynamically Triangulated Random Surfaces embedded in three dimensions with an extrinsic curvature dependent action. We analyze several observables in the crossover regime and discuss whether or not our observations are indicative of the presence of a phase transition.Comment: (Contribution to Lattice 92 Proceedings.) Latex file (5 pages), requires espcrc2.sty. 2 figures not included. Syracuse preprint SU-HEP-4241-52

The Phase Diagram of Fluid Random Surfaces with Extrinsic Curvature

We present the results of a large-scale simulation of a Dynamically Triangulated Random Surface with extrinsic curvature embedded in three-dimensional flat space. We measure a variety of local observables and use a finite size scaling analysis to characterize as much as possible the regime of crossover from crumpled to smooth surfaces.Comment: 29 pages. There are also 19 figures available from the authors but not included here - sorr

Universality and its Origins at the Amorphous Solidification Transition

Systems undergoing an equilibrium phase transition from a liquid state to an amorphous solid state exhibit certain universal characteristics. Chief among these are the fraction of particles that are randomly localized and the scaling functions that describe the order parameter and (equivalently) the statistical distribution of localization lengths for these localized particles. The purpose of this Paper is to discuss the origins and consequences of this universality, and in doing so, three themes are explored. First, a replica-Landau-type approach is formulated for the universality class of systems that are composed of extended objects connected by permanent random constraints and undergo amorphous solidification at a critical density of constraints. This formulation generalizes the cases of randomly cross-linked and end-linked macromolecular systems, discussed previously. The universal replica free energy is constructed, in terms of the replica order parameter appropriate to amorphous solidification, the value of the order parameter is obtained in the liquid and amorphous solid states, and the chief universal characteristics are determined. Second, the theory is reformulated in terms of the distribution of local static density fluctuations rather than the replica order parameter. It is shown that a suitable free energy can be constructed, depending on the distribution of static density fluctuations, and that this formulation yields precisely the same conclusions as the replica approach. Third, the universal predictions of the theory are compared with the results of extensive numerical simulations of randomly cross-linked macromolecular systems, due to Barsky and Plischke, and excellent agreement is found.Comment: 10 pages, including 3 figures (REVTEX

Domain growth and aging scaling in coarsening disordered systems

Using extensive Monte Carlo simulations we study aging properties of two disordered systems quenched below their critical point, namely the two-dimensional random-bond Ising model and the three-dimensional Edwards-Anderson Ising spin glass with a bimodal distribution of the coupling constants. We study the two-times autocorrelation and space-time correlation functions and show that in both systems a simple aging scenario prevails in terms of the scaling variable $L(t)/L(s)$, where $L$ is the time-dependent correlation length, whereas $s$ is the waiting time and $t$ is the observation time. The investigation of the space-time correlation function for the random-bond Ising model allows us to address some issues related to superuniversality.Comment: 8 pages, 9 figures, to appear in European Physical Journal

Staggered fermions and chiral symmetry breaking in transverse lattice regulated QED

Staggered fermions are constructed for the transverse lattice regularization scheme. The weak perturbation theory of transverse lattice non-compact QED is developed in light-cone gauge, and we argue that for fixed lattice spacing this theory is ultraviolet finite, order by order in perturbation theory. However, by calculating the anomalous scaling dimension of the link fields, we find that the interaction Hamiltonian becomes non-renormalizable for $g^2(a) > 4\pi$, where $g(a)$ is the bare (lattice) QED coupling constant. We conjecture that this is the critical point of the chiral symmetry breaking phase transition in QED. Non-perturbative chiral symmetry breaking is then studied in the strong coupling limit. The discrete remnant of chiral symmetry that remains on the lattice is spontaneously broken, and the ground state to lowest order in the strong coupling expansion corresponds to the classical ground state of the two-dimensional spin one-half Heisenberg antiferromagnet.Comment: 30 pages, UFIFT-HEP-92-1

Self- generated disorder and structural glass formation in homopolymer globules

We have investigated the interrelation between the spin glasses and the structural glasses. Spin glasses in this case are random magnets without reflection symmetry (e.g. $p$ - spin interaction spin glasses and Potts glasses) which contain quenched disorder, whereas the structural glasses are here exemplified by the homopolymeric globule, which can be viewed as a liquid of connected molecules on nano scales. It is argued that the homopolymeric globule problem can be mapped onto a disorder field theoretical model whose effective Hamiltonian resembles the corresponding one for the spin glass model. In this sense the disorder in the globule is self - generated (in contrast to spin glasses) and can be related with competitive interactions (virial coefficients of different signs) and the chain connectivity. The work is aimed at giving a quantitative description of this analogy. We have investigated the phase diagram of the homopolymeric globule where the transition line from the liquid to glassy globule is treated in terms of the replica symmetry breaking paradigm. The configurational entropy temperature dependence is also discussed.Comment: 22 pages, 4 figures, submitted to Phys. Rev.

Parallel Excluded Volume Tempering for Polymer Melts

We have developed a technique to accelerate the acquisition of effectively uncorrelated configurations for off-lattice models of dense polymer melts which makes use of both parallel tempering and large scale Monte Carlo moves. The method is based upon simulating a set of systems in parallel, each of which has a slightly different repulsive core potential, such that a thermodynamic path from full excluded volume to an ideal gas of random walks is generated. While each system is run with standard stochastic dynamics, resulting in an NVT ensemble, we implement the parallel tempering through stochastic swaps between the configurations of adjacent potentials, and the large scale Monte Carlo moves through attempted pivot and translation moves which reach a realistic acceptance probability as the limit of the ideal gas of random walks is approached. Compared to pure stochastic dynamics, this results in an increased efficiency even for a system of chains as short as $N = 60$ monomers, however at this chain length the large scale Monte Carlo moves were ineffective. For even longer chains the speedup becomes substantial, as observed from preliminary data for $N = 200$

Computer Simulations of Supercooled Liquids and Glasses

After a brief introduction to the dynamics of supercooled liquids, we discuss some of the advantages and drawbacks of computer simulations of such systems. Subsequently we present the results of computer simulations in which the dynamics of a fragile glass former, a binary Lennard-Jones system, is compared to the one of a strong glass former, SiO_2. This comparison gives evidence that the reason for the different temperature dependence of these two types of glass formers lies in the transport mechanism for the particles in the vicinity of T_c, the critical temperature of mode-coupling theory. Whereas the one of the fragile glass former is described very well by the ideal version of mode-coupling theory, the one for the strong glass former is dominated by activated processes. In the last part of the article we review some simulations of glass formers in which the dynamics below the glass transition temperature was investigated. We show that such simulations might help to establish a connection between systems with self generated disorder (e.g. structural glasses) and quenched disorder (e.g. spin glasses).Comment: 37 pages of Latex, 11 figures, to appear as a Topical Review article in J. Phys.: Condens. Matte