The influence of boundaries on high pressure melting experiments

At low pressure, free surfaces play a crucial role in the melting transition. Under pressure, the surface of the sample is acted upon by some pressure transmitting medium. To examine the effect of this medium on melting, we performed Monte Carlo simulations of a system of argon atoms in the form of a slab with two boundaries. We examined two cases, one with a soft and the other with a rigid medium at the boundaries. We found that in the presence of a rigid medium, melting resembles the mechanical lattice instability found in a surface-free solid. With a soft medium at the boundary, melting begins at the surface and at a lower temperature. The relevance of these results to experiment is discussed.Comment: 4 pages, 5 figure

Accurate modeling approach for the structural comparison between monolayer polymer tubes and single-walled nanotubes

In a recent computational study, we found highly structured ground states for coarse-grained polymers adsorbed to ultrathin nanowires in a certain model parameter region. Those tubelike configurations show, even at a first glance, exciting morphological similarities to known atomistic nanotubes such as single-walled carbon nanotubes. In order to explain those similarities in a systematic way, we performed additional detailed and extensive simulations of coarse-grained polymer models with various parameter settings. We show this here and explain why standard geometrical models for atomistic nanotubes are not suited to interpret the results of those studies. In fact, the general structural behavior of polymer nanotubes, as well as specific previous observations, can only be explained by applying recently developed polyhedral tube models.Comment: Proceedings of the 24th Workshop on Recent Developments in Computer Simulation Studies in Condensed Matter Physics, Feb 21-25, 2011, Athens, Georgia, US

Efficient Hopfield pattern recognition on a scale-free neural network

Neural networks are supposed to recognise blurred images (or patterns) of $N$ pixels (bits) each. Application of the network to an initial blurred version of one of $P$ pre-assigned patterns should converge to the correct pattern. In the "standard" Hopfield model, the $N$ "neurons'' are connected to each other via $N^2$ bonds which contain the information on the stored patterns. Thus computer time and memory in general grow with $N^2$. The Hebb rule assigns synaptic coupling strengths proportional to the overlap of the stored patterns at the two coupled neurons. Here we simulate the Hopfield model on the Barabasi-Albert scale-free network, in which each newly added neuron is connected to only $m$ other neurons, and at the end the number of neurons with $q$ neighbours decays as $1/q^3$. Although the quality of retrieval decreases for small $m$, we find good associative memory for $1 \ll m \ll N$. Hence, these networks gain a factor $N/m \gg 1$ in the computer memory and time.Comment: 8 pages including 4 figure

High-Temperature Series Analyses of the Classical Heisenberg and XY Model

Although there is now a good measure of agreement between Monte Carlo and high-temperature series expansion estimates for Ising ($n=1$) models, published results for the critical temperature from series expansions up to 12{\em th} order for the three-dimensional classical Heisenberg ($n=3$) and XY ($n=2$) model do not agree very well with recent high-precision Monte Carlo estimates. In order to clarify this discrepancy we have analyzed extended high-temperature series expansions of the susceptibility, the second correlation moment, and the second field derivative of the susceptibility, which have been derived a few years ago by L\"uscher and Weisz for general $O(n)$ vector spin models on $D$-dimensional hypercubic lattices up to 14{\em th} order in $K \equiv J/k_B T$. By analyzing these series expansions in three dimensions with two different methods that allow for confluent correction terms, we obtain good agreement with the standard field theory exponent estimates and with the critical temperature estimates from the new high-precision MC simulations. Furthermore, for the Heisenberg model we reanalyze existing series for the susceptibility on the BCC lattice up to 11{\em th} order and on the FCC lattice up to 12{\em th} order.Comment: 15 pages, Latex, 2 PS figures not included. FUB-HEP 18/92 and HLRZ 76/9

Series Approach to the Randomly Diluted Elastic Network

Series expansions in powers of the concentration p for elastic and other susceptibilities of randomly diluted elastic networks have been generated for a bond-bending model on a honeycomb lattice up to 13th order, and for the central-force model on a triangular lattice up to 22nd order, in p. Critical exponents for both models and the critical threshold of the central-force problem have been estimated by Padé-approximant-analysis techniques. We obtain exponent estimates that are consistent with scaling relations and other calculations. For the bond-bending model, the effective splay elastic constant scales like L−φsp/ν with φsp=1.20±0.015. For central-force elastic percolation, we find β+γ=1.9±0.2 and ν=1.1±0.2