The heat capacity and isomer distributions of the 38-atom Lennard-Jones cluster have been calculated in the canonical ensemble using parallel tempering Monte Carlo methods. A distinct region of temperature is identified that corresponds to equilibrium between the global minimum structure and the icosahedral basin of structures. This region of temperatures occurs below the melting peak of the heat capacity and is accompanied by a peak in the derivative of the heat capacity with temperature. Parallel tempering is shown to introduce correlations between results at different temperatures. A discussion is given that compares parallel tempering with other related approaches that ensure ergodic simulations.

We study the 38-atom Lennard-Jones cluster with parallel tempering Monte Carlo methods in the microcanonical and molecular dynamics ensembles. A new Monte Carlo algorithm is presented that samples rigorously the molecular dynamics ensemble for a system at constant total energy, linear and angular momenta. By combining the parallel tempering technique with molecular dynamics methods, we develop a hybrid method to overcome quasiergodicity and to extract both equilibrium and dynamical properties from Monte Carlo and molecular dynamics simulations. Several thermodynamic, structural, and dynamical properties are investigated for LJ 38 , including the caloric curve, the diffusion constant and the largest Lyapunov exponent. The importance of insuring ergodicity in molecular dynamics simulations is illustrated by comparing the results of ergodic simulations with earlier molecular dynamics simulations.

Previous heat capacity estimators useful in path integral simulations have variances that grow with the number of path variables included. In the present work a new specific heat estimator for Fourier path integral Monte Carlo simulations is derived using methods similar to those used in developing virial energy estimators. The resulting heat capacity estimator has a variance that is roughly independent of the number of Fourier coefficients (k max ) included, and the asymptotic convergence rate is shown to be proportional to 1/k max 2 when partial averaging is included. Quantum Monte Carlo simulations are presented to test the estimator using two one-dimensional models and for Lennard-Jones representations of Ne 13 . For finite k max , using numerical methods, the calculated heat capacity is found to diverge at low temperatures for the potential functions studied in this work. Extrapolation methods enable useful results to be determined over a wide temperature range.

An improved inference method for densely connected systems is presented. The approach is based on passing condensed messages between variables, representing macroscopic averages of microscopic messages. We extend previous work that showed promising results in cases where the solution space is contiguous to cases where fragmentation occurs. We apply the method to the signal detection problem of Code Division Multiple Access (CDMA) for demonstrating its potential. A highly efficient practical algorithm is also derived on the basis of insight gained from the analysis.

We present finite-size scaling and phenomenological renormalization equations for calculations of the critical points of the electronic structure of atoms and molecules. Results show that the method is efficient and very accurate for estimating the critical screening length for one-electron screened Coulomb potentials and the critical nuclear charge for two-electron atoms. The method has potential applicability for many-body quantum systems. [S0031-9007 (97)04408-6] PACS numbers: 31.15. -p, 05.70.Jk