Wolfhard Janke

Multicanonical Monte Carlo simulations

Canonical Monte Carlo simulations of disordered systems like spin glasses and systems undergoing first-order phase transitions are severely hampered by rare event states which lead to exponentially diverging autocorrelation times with increasing system size and hence to exponentially large statistical errors. One possibility to overcome this problem is the multicanonical reweighting method. Using standard local update algorithms it could be demonstrated that the dependence of autocorrelation times on the system size V is well described by a less divergent power law, τ∝Vα, with 1<α<3, depending on the system. After a brief review of the basic ideas, combinations of multicanonical reweighting with non-local update algorithms will be discussed. With the multibondic algorithm, which combines multicanonical reweighting with cluster updates, the dynamical exponent α can be reduced to unity, the optimal value one would expect from a random walk argument. Asymptotically for large system sizes the multibondic algorithm therefore always performs better than the standard multicanonical method. Finally it is shown that a combination with multigrid update techniques improves the performance of multicanonical simulations by roughly one order of magnitude, uniformly for all system sizes.

Critical exponents of the classical three-dimensional Heisenberg model: A single-cluster Monte Carlo study.

We have simulated the three-dimensional Heisenberg model on simple cubic lattices, using the single-cluster Monte Carlo update algorithm. The expected pronounced reduction of critical slowing down at the phase transition is verified. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors. In one set of simulations we employ the usual finite-size scaling methods to compute the critical exponents \ensuremath{\nu},\ensuremath{\alpha},\ensuremath{\beta},\ensuremath{\gamma},\ensuremath{\eta} from a few measurements in the vicinity of the critical point, making extensive use of histogram reweighting and optimization techniques. In another set of simulations we report measurements of improved estimators for the spatial correlation length and the susceptibility in the high-temperature phase, obtained on lattices with up to

Multicanonical chain-growth algorithm.

{100}^{3}

Convergent Strong-Coupling Expansions from Divergent Weak-Coupling Perturbation Theory

spins. This enables us to compute independent estimates of \ensuremath{\nu} and \ensuremath{\gamma} from power-law fits of their critical divergencies.

Thermodynamics of lattice heteropolymers.

We present a temperature-independent Monte Carlo method for the determination of the density of states of lattice proteins that combines the fast ground-state search strategy of the new pruned-enriched Rosenbluth chain-growth method and multicanonical reweighting for sampling the complete energy space. Since the density of states contains all energetic information of a statistical system, we can directly calculate the mean energy, specific heat, Helmholtz free energy, and entropy for all temperatures. We apply this method to lattice proteins consisting of hydrophobic and polar monomers, and for the examples of sequences considered, we identify the transitions between native, globule, and random coil states. Since no special properties of heteropolymers are involved in this algorithm, the method applies to polymer models as well.

Microcanonical analyses of peptide aggregation processes.

As an application of a recently developed variational perturbation theory we find the first 22 terms of the convergent strong-coupling series expansion for the ground state energy of the quartic anharmonic oscillator.

Multibondic cluster algorithm for Monte Carlo simulations of first-order phase transitions.

We calculate thermodynamic quantities of hydrophobic-polar (HP) lattice proteins by means of a multicanonical chain-growth algorithm that connects the new variants of the Pruned-Enriched Rosenbluth Method and flat histogram sampling of the entire energy space. Since our method directly simulates the density of states, we obtain results for thermodynamic quantities of the system for all temperatures. In particular, this algorithm enables us to accurately simulate the usually difficult accessible low-temperature region. Therefore, it becomes possible to perform detailed analyses of the low-temperature transition between ground states and compact globules.

Conformational transitions of nongrafted polymers near an absorbing substrate.

We propose the use of microcanonical analyses for numerical studies of peptide aggregation transitions. Performing multicanonical Monte Carlo simulations of a simple hydrophobic-polar continuum model for interacting heteropolymers of finite length, we find that the microcanonical entropy behaves convex in the transition region, leading to a negative microcanonical specific heat. As this effect is also seen in first-order-like transitions of other finite systems, our results provide clear evidence for recent hints that the characterization of phase separation in first-order-like transitions of finite systems profits from this microcanonical view.

Microscopic mechanism of specific peptide adhesion to semiconductor substrates.

Inspired by the multicanonical approach to simulations of first-order phase transitions we propose for

Make Life Simple: Unleash the Full Power of the Parallel Tempering Algorithm

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