The present work deals with relaxation dynamics on complex energy landscapes.
The state space of a complex system possesses, as a hallmark,
the multitude of local minima separated by higher states, called
barrier states. This feature gives rise to a host of non-equilibrium phenomena.
From case to case, for different complex systems, ranging from atomic clusters, spin glasses and proteins
to neural networks or financial markets, the key quantities like energy and temperature
may have different meanings, though their functionality is the same.
The numerical handling of relaxational dynamics in such complex systems, even for relatively small sizes,
poses a tough challenge if the entire state space is to be considered.
Here, state space sampling procedures are introduced that provide an accurate enough description
for the low temperature dynamics, using small subsets from the original state space.
As test cases, short range Ising spin systems were considered.
The samples - depending on the way they are constructed - provide either lower bounds for
the largest relaxation timescales in a quasi-ergodic component of
the state space or the isothermal relaxation of the mean energy, like in the proposed DRS method.
Upon the latter procedure, a parallel heuristic is built which gives the possibility of handling large samples.
The collected structural data provides information of the state space topology in systems with
different levels of frustration, like disordered ferromagnets and spin glasses. It provides insights into the
focusing/anti-focusing types of landscapes, which give rise to different ground state accessibilities.
For the large samples, the domain formation and growth has been analysed and compared with existing experimental
and numerical data in literature.
The algorithms proposed here become more and more accurate as the temperature is decreased and therefore
they can provide an alternative to the classical Monte Carlo approach for this temperature range.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-200800688 |
| Date | 22 May 2008 |
| Creators | Nemnes, George Alexandru |
| Contributors | TU Chemnitz, Fakultät für Naturwissenschaften, Prof. Dr. Karl Heinz Hoffmann, Prof. Dr. Karl Heinz Hoffmann, Prof. Dr. Michael Schreiber, Prof. Dr. Paolo Sibani |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf, text/plain, application/zip |
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