Dynamical Spin Systems
Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
As of today, there is still no general theory that can be applied to understand the dynamics innon-equilibrium systems and usually one has to turn to approximations and simulations in orderto extract any information out of a system. In fact, there are only a few known examples, such asthe asymmetric simple exclusion process and a family of related models where analytical resultshave been proven successful.
In this thesis we will start by studying the dynamics in three different classical spin systems.The common factor in all of them is that we consider quenches to low temperatures. Before thequench takes place the system is in equilibrium at a high temperature, usually taken to be atinfinity. For systems in one dimension, this process can be described in terms of domains evolvingtowards a new equilibrium configuration. The approach of elucidating the dynamics starts with themaster equation. This can however be exactly solved only in a very few cases. One approximationthat can be made in the context of quenches is the independent interval approximation (IIA),which captures the main features of the dynamics. The IIA is proven to be exact when domainsonly monotonically increase its length and never split up. But even in those cases where it is notexact it gives the main qualitative behavior of the system in the asymptotic limit.
The three spin models studied, all have exactly determinable steady states (which in fact areequilibrium configurations in two of the cases). In this thesis, we introduce a new spin model,in which the dynamics is truly irreversible and the steady state is not exactly determinable. Wecall it the Modified East model. Using the IIA and a generating function approach we are able tofind some analytical properties of the system. These results agree well with simulations at hightemperatures, surprisingly, since the IIA is only exact at very low temperatures. We have not beenable to verify analytical predictions with simulations in the limit of zero temperature but we canargue that it should still be a good match.
Place, publisher, year, edition, pages
2014. , 55 p.
Non-equilibrium statistical physics, Quenches, Ising, Domain-length distribution, Glassy systems, East model.
Other Physics Topics
IdentifiersURN: urn:nbn:se:su:diva-104336OAI: oai:DiVA.org:su-104336DiVA: diva2:722719
Krishnamurthy, Supriya, Associate Professor