Computer Simulations of Quantum Chains

We report recent progress in computer simulations of quantum systems described in the path-integral formulation. For the example of the $\phi^4$ quantum chain we show that the accuracy of the simulation may greatly be enhanced by a combination of multigrid update techniques with a refined discretization scheme. This allows us to assess the accuracy of a variational approximation.Comment: 5 pages, LaTeX + 2 postscript figures. Talk presented by TS at "Path Integrals from meV to MeV: Dubna '96". See also http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm

High-Temperature Series Expansions for Random Potts Models

We discuss recently generated high-temperature series expansions for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices. Using the star-graph expansion technique quenched disorder averages can be calculated exactly for arbitrary uncorrelated coupling distributions while keeping the disorder strength p as well as the dimension d as symbolic parameters. We present analyses of the new series for the susceptibility of the Ising (q=2) and 4-state Potts model in three dimensions up to order 19 and 18, respectively, and compare our findings with results from field-theoretical renormalization group studies and Monte Carlo simulations.Comment: 16 pages,cmp209.sty (included), 9 postscript figures, author information under http://www.physik.uni-leipzig.de/index.php?id=2

Conformational Transitions of Non-Grafted Polymers Near an Adsorbing Substrate

We have performed multicanonical chain-growth simulations of a polymer interacting with an adsorbing surface. The polymer, which is not explicitly anchored at the surface, experiences a hierarchy of phase transitions between conformations binding and non-binding with the substrate. We discuss the phase diagram in the temperature-solubility plane and highlight the transition ``path'' through the free-energy landscape.Comment: 4 pages, revtex.cls, 10 postscript figures, author information under http://www.physik.uni-leipzig.de/index.php?id=2

Exploring different regimes in finite-size scaling of the droplet condensation-evaporation transition

We present a finite-size scaling analysis of the droplet condensation-evaporation transition of a lattice gas (in two and three dimensions) and a Lennard-Jones gas (in three dimensions) at fixed density. Parallel multicanonical simulations allow sampling of the required system sizes with precise equilibrium estimates. In the limit of large systems, we verify the theoretical leading-order scaling prediction for both the transition temperature and the finite-size rounding. In addition, we present an emerging intermediate scaling regime, consistent in all considered cases and with similar recent observations for polymer aggregation. While the intermediate regime locally may show a different effective scaling, we show that it is a gradual crossover to the large-system scaling behavior by including empirical higher-order corrections. This implies that care has to be taken when considering scaling ranges, possibly leading to completely wrong predictions for the thermodynamic limit. In this study, we consider a crossing of the phase boundary orthogonal to the usual fixed temperature studies. We show that this is an equivalent approach and, under certain conditions, may show smaller finite-size corrections.Comment: 12 pages, 9 figures, to appear in Phys. Rev.

Conformational transitions in random heteropolymer models

We study the conformational properties of heteropolymers containing two types of monomers A and B, modeled as self-avoiding random walks on a regular lattice. Such a model can describe in particular the sequences of hydrophobic and hydrophilic residues in proteins (K.F. Lau and K.A. Dill, Macromolecules {\bf 22}, 3986 (1989)) and polyampholytes with oppositely charged groups (Y. Kantor and M. Kardar, Europhys. Lett.{\bf 28}, 169 (1994)). Treating the sequences of the two types of monomers as quenched random variables, we provide a systematic analysis of possible generalizations of this model. To this end we apply the pruned-enriched Rosenbluth chain-growth algorithm (PERM), which allows us to obtain the phase diagrams of extended and compact states coexistence as function of both the temperature and fraction of A and B monomers along the heteropolymer chain