| ESPERIMENTO BO62, RESPONSABILE: Paolo Pasini
L’attività dell’iniziativa specifica BO12 consiste nello
sviluppo di modelli e metodi di calcolo per lo studio di
problemi rilevanti nella meccanica statistica, meccanica
quantistica e nella fisica della materia condensata.
In particolare vengono usati metodi di meccanica statistica per studiare la criticità autoorganizzata (es. sandpiles e
valanghe), biopolimeri (denaturazione del DNA e RNA) e
topologia dei polimeri. Lo studio di alcuni di questi
sistemi avviene anche mediante simulazioni Monte Carlo.
Simulazioni Monte Carlo vengono anche usate per studiare
transizioni di fase ordine-disordine in modelli su reticolo
di sistemi anisotropi (es. cristalli liquidi). Di
particolare rilevanza è lo studio dei difetti topologici
indotti dalla interazione particella-particella, dal confinamento e dalle caratteristiche alle superfici.
Viene anche impiegata il metodo Density Matrix
Renormalization Group per lo studio di problemi quantistici
a molti-corpi e di elettroni correlati. Tale metodo è
applicabile allo studio di sistemi su reticolo sia nel caso di elettroni che nel caso di spin.
| OBIETTIVI DELL'ESPERIMENTO BO62
|MODELS AND MONTE CARLO SIMULATIONS IN STATISTICAL AND QUANTUM MECHANICS.
The main interest of the groups involved in the project is to develop models and computational methods to study problems of relevance in statistical and quantum mechanics and condensed matter. The research activity can be summarized in four main tasks:
i) Statistical mechanics out of equilibrium;
ii) Polymers and heteropolymers.
iii) Density Matrix Renormalitazion Group
iv) Monte Carlo simulations of lattice spin models
The aim of the project for the first task is to continue the investigation of the correspondence between turbulence and sandpile quantities, correspondence which has demonstrated that the Bak, Tang and Wiesenfeld prototype model of self-organized criticality provides an analog of several turbulent phenomena. Particular attention will be devoted to a better understanding of the multiscaling of avalanches.
For the second task the study of the diblock copolymer zipping transition has suggested to look in a new perspective at the geometrical properties of the classical self-avoiding walk (SAW) problem. Using multiple Markov chain Monte Carlo methods, it has been shown that the nearest neighbor contacts between the two halves of an N-step SAW provide a very unusual example of set with scaling random geometry. For N approaching infinity these contacts are in finite number, while their radius of gyration is power law distributed with a novel exponent \tau, never studied before in the SAW context. This contrasts with the case of standard fractal sets, in which scale invariance is accompanied by the number of elements becoming infinite. It has also been found that, since \tau exceeds unity, there exists a continuum of diverging characteristic length scales in the SAW. A transfer matrix numerical study at zero temperature of directed polymers in the presence of tilted columnar disorder in two dimensions has shown that minimal energy differences obey a multiscaling at short distances which crosses over to
simple scaling at large distances. The scenario is analogous to that of structure functions in bifractal Burgers' turbulence. Some scaling properties could also be determined (presumably, exactly) based on extreme value statistics arguments. Besides being of general interest for the theory of the Burgers' and KPZ equations, the results are expected to be relevant also for the physics of flux lines in type II superconductors with splayed defects produced by ion bombardment. Within this framework we shall continue the analysis of the diblock copolymer zipping and collapse transitions in three dimensions and a systematic study of models to describe the DNA denaturation.
The Density Matrix Renormalization Group ( DMRG) method (third task) is a powerful numerical method for studying the quantum many-body problem and the electron correlation problem; problems which are a big challenge from a computational point of view. We plan to apply the DMRG method to study lattice systems, both in the case of electrons and in the case of spins. An interesting case for lattice electronic systems is given by a electronic potential of the square well where it would be possible to give a phase diagram at zero temperature with a possible transition from a phase separation, which is certainly present for large (and negative) values of the interaction, to a superconducting state. We want also to study a one-dimensional antiferromagnetic spin chain in the presence of a staggered magnetic field, comparing the DMRG results with mean field approximations based on the non linear sigma model.
Within the framework of the fourth task we deal with lattice spin models for studying anisotropic systems and the group has performed a number of investigations on different models and systems in the last few years. These spin models provide an interesting and useful approach for investigating various aspects of the physics of liquid crystals. In particular, mainly due to the simplicity of the models and consequently to the larger number of particles which can be treated in comparison with more realistic potentials, they also allow to tackle by computer simulations problems not easily accessible by theoretical approaches. In particular can be investigated confined systems, systems containing a percentage of disorder and structures of topological defects for which large lattices are needed. We plan to devote more attention to the formation of topological defects which is a very common feature of phase transitions, both in condensed matter and particle physics models. We have recently shown that lattice simulations are suitable to clarify the nature of the hedgehog (monopole) core in magnetic and nematic cases and to reproduce stable point defects in a nematic film with hybrid boundary conditions. Our aim will be to study now more complex systems like the biaxial one and the evolution of entangled strings. Another important problem we wish to investigate is the memory effect of liquid crystals in random geometries where the nematics seems to acquire typical glassy properties. To investigate this problem we shall perform latttice simulations of the Sprinkled Silica Spin (SSS) model we have recently proposed.
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