Monte Carlo Study of Pure-Phase Cumulants of 2D q-State Potts Models

We performed Monte Carlo simulations of the two-dimensional q-state Potts model with q=10, 15, and 20 to study the energy and magnetization cumulants in the ordered and disordered phase at the first-order transition point $\beta_t$. By using very large systems of size 300 x 300, 120 x 120, and 80 x 80 for q=10, 15, and 20, respectively, our numerical estimates provide practically (up to unavoidable, but very small statistical errors) exact results which can serve as a useful test of recent resummed large-q expansions for the energy cumulants by Bhattacharya `et al.' [J. Phys. I (France) 7 (1997) 81]. Up to the third order cumulant and down to q=10 we obtain very good agreement, and also the higher-order estimates are found to be compatible.Comment: 18 pages, LaTeX + 2 postscript figures. To appear in J. Phys. I (France), May 1997 See also http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm

Polymer simulation by means of tree data-structures and a parsimonious Metropolis algorithm

We show how a Monte Carlo method for generating self-avoiding walks on lattice geometries which employs a binary-tree data structure can be adapted for hard-sphere polymers with continuous degrees of freedom. Data suggests that the time per Monte Carlo move scales logarithmically with polymer size. We combine the method with a variant of the Metropolis algorithm and preserve this scaling for Lennard-Jones polymers with untruncated monomer-monomer interaction. We further show how the replica-exchange method can be adapted for the same purpose.Comment: 10 pages, 10 figure

Correlation Length From Cluster-Diameter Distribution

We report numerical estimates of correlation lengths in 2D Potts models from the asymptotic decay of the cluster-diameter distribution. Using this observable we are able to verify theoretical predictions for the correlation length in the disordered phase at the transition point for $q=10$, 15, and 20 with an accuracy of about $1$. This is a considerable improvement over previous measurements using the standard (projected) two-point function.Comment: 4 pages, PostScript, contribution to LATTICE95. See also http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm

Advanced multicanonical Monte Carlo methods for efficient simulations of nucleation processes of polymers

The investigation of freezing transitions of single polymers is computationally demanding, since surface effects dominate the nucleation process. In recent studies we have systematically shown that the freezing properties of flexible, elastic polymers depend on the precise chain length. Performing multicanonical Monte Carlo simulations, we faced several computational challenges in connection with liquid-solid and solid-solid transitions. For this reason, we developed novel methods and update strategies to overcome the arising problems. We introduce novel Monte Carlo moves and two extensions to the multicanonical method.Comment: 10 pages, 11 figure

Identification of Characteristic Protein Folding Channels in a Coarse-Grained Hydrophobic-Polar Peptide Model

Folding channels and free-energy landscapes of hydrophobic-polar heteropolymers are discussed on the basis of a minimalistic off-lattice coarse-grained model. We investigate how rearrangements of hydrophobic and polar monomers in a heteropolymer sequence lead to completely different folding behaviors. Studying three exemplified sequences with the same content of hydrophobic and polar residues, we can reproduce within this simple model two-state folding, folding through intermediates, as well as metastability.Comment: 26 pages, 6 figure

Different Kinds of Protein Folding Identified with a Coarse-Grained Heteropolymer Model

Applying multicanonical simulations we investigated folding properties of off-lattice heteropolymers employing a mesoscopic hydrophobic-polar model. We study for various sequences folding channels in the free-energy landscape by comparing the equilibrium conformations with the folded state in terms of an angular overlap parameter. Although all investigated heteropolymer sequences contain the same content of hydrophobic and polar monomers, our analysis of the folding channels reveals a variety of characteristic folding behaviors known from realistic peptides.Comment: 3 pages, 2 figure

Multibondic Cluster Algorithm

Inspired by the multicanonical approach to simulations of first-order phase transitions we propose for $q$-state Potts models a combination of cluster updates with reweighting of the bond configurations in the Fortuin-Kastelein-Swendsen-Wang representation of this model. Numerical tests for the two-dimensional models with $q=7, 10$ and $20$ show that the autocorrelation times of this algorithm grow with the system size $V$ as $\tau \propto V^\alpha$, where the exponent takes the optimal random walk value of $\alpha \approx 1$.Comment: 3 pages, uuencoded compressed postscript file, contribution to the LATTICE'94 conferenc

Ordered vs Disordered: Correlation Lengths of 2D Potts Models at \beta_t

We performed Monte Carlo simulations of two-dimensional $q$-state Potts models with $q=10,15$, and $20$ and measured the spin-spin correlation function at the first-order transition point $\beta_t$ in the disordered and ordered phase. Our results for the correlation length $\xi_d(\beta_t)$ in the disordered phase are compatible with an analytic formula. Estimates of the correlation length $\xi_o(\beta_t)$ in the ordered phase yield strong numerical evidence that $R \equiv \xi_o(\beta_t)/\xi_d(\beta_t) = 1$.Comment: 3 pages, uuencoded compressed postscript file, contribution to the LATTICE'94 conferenc