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Long flexible polymer chains can be modelled as self-avoiding random walks and their properties analyzed by exploiting the polymer-magnet analogy and using field theoretical tools. We discuss the behavior of chains in an infinite unbounded space and the interaction of chains with impenetrable boundaries, such as those of mesoscopic spheres and cylinders. This is relevant for colloidal particles immersed...
We present basic definitions and various examples for random walk models. The random walk representation by Brydges, Fröhlich and Spencer for the Green functions of the N-component field theory is discussed. As an application it is shown that the continuum limit of the Φ4 model is trivial in D>4 dimensions.
Polymer expansion is a useful tool in statistical mechanics and Euclidean field theory. Various examples of polymer systems including high and low temperature expansions of the Ising model, N-component field theory and lattice gauge field theory are presented. We discuss the concepts of Kirkwood-Salsburg equations, Moebius transform, cluster expansion formula of the free energy and thermodynamic limit.
The generic relation between continuous polymers and zero-component Euclidean field-theories is reviewed, and exemplified by polymers with contact and Coulomb interactions. An analogous relation on the lattice is also discussed, relating the statistics of self-avoiding walks to a zero-component spin-model.
We present a brief tutorial introduction into the quantum Hamiltonian formalism for stochastic many-body systems defined in terms of a master equation for their time evolution. These models describe interacting classical particle systems where particles hop on a lattice and may undergo reactions such as A+A→0. The quantum Hamiltonian formalism for the master equation provides a convenient general...
Path integral techniques in collective fields are shown to be a useful analytical tool to reformulate a field theory defined in terms of microscopic quark (gluon) degrees of freedom as an effective theory of collective boson (meson) fields. For illustrations, the path integral bosonization approach is applied to derive a (non)linear σ model from a Nambu-Jona-Lasinio (NJL) quark model. The method can...
The method of path integral hadronization is applied to a local quark-diquark toy model in order to derive an effective chiral meson-baryon Lagrangian. Further generalizations to models including both scalar and axial-vector diquarks as well as nonlocal interactions are discussed.
The Hybrid Monte Carlo (HMC) algorithm currently is the favorite scheme to simulate quantum chromodynamics including dynamical fermions. In this talk—which is intended for a non-expert audience—I want to bring together methodical and practical aspects of the HMC for full QCD simulations. I will comment on its merits and shortcomings, touch recent improvements and try to forecast its efficiency and...
The use of the Hybrid Monte Carlo method in simulating off-lattice polymer chains is discussed. I focus on the problem of finding efficient algorithms for long flexible chains. To speed up the simulation of such chains the Fourier acceleration technique is used. Numerical results are presented for four models with different repulsive interactions between the monomers.
Folding properties of two simple off-lattice protein models in two and three dimensions, respectively, are analyzed numerically by using the simulated-tempering method. Both models have two types of “amino acids”, hydrophobic and hydrophilic. In the two-dimensional model, a total of 300 randomly selected sequences with 20 monomers are studied. About 10% of these meet criteria for good folders. A statistical...
The dynamics of phase transitions plays a crucial rôle in the so-called interface between high energy particle physics and cosmology. Many of the interesting results generated during the last fifteen years or so rely on simplified assumptions concerning the complex mechanisms typical of nonequilibrium field theories. After reviewing well-known results concerning the dynamics of first and second order...
We give a brief review of neural networks. This includes views and features about the general concept, the modelling problem for Neural Networks and their treatment with statistical physics methods. Their use as Expert Systems is illustrated for the application of Multilayer Perceptrons to High Energy Physics data analysis. Finally, we focus on recent statistical insight, which under certain conditions...
Quantum chromodynamics has a rather complicated phase structure. The finite temperature, chiral phase structure depends on the number of flavours and to a large extent on the particular values of the fermion masses. For two massless flavours there is a true second order transition. It has been argued that this transition belongs to the universality class of the three-dimensional O(4) spin model. The...
We summarize recent work showing how the Thermodynamic Bethe Ansatz may be used to study the finite-density first-order phase transition in the Gross-Neveu model. The application to trans-polyacetylene is discussed, and the significance of the results is addressed.
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