Most current research on ising model ground state configuration

[Key01023]

 

 

Hi,

I want to do mathematical research (algorithm construction and mathematical analysis) on ising model ground state configuration. From what I know, the state of art research is using graph theory formalism.

 

Could someone give me some advice on how to learn this subject (say, what books or papers to read) to a research level from a basic undergraduate math background?

 

Thanks

Edited October 3, 2013 by Key01023

[Enthalpy]

Hi Key010123, welcome here!

 

Please forgive my nonconstructive answer, but is research on the Ising model still useful in 2013?

 

Meanwhile Mankind has observed exactly (you know, Weiss, Bloch, all that stuff) thanks to the proper apparatus what makes a ferromagnetic material, and very little "modelling" is necessary in addition to the observation...

 

Why should time be invested in an a priori model that does not reflect the microscopic observations, does not make more accurate predictions, nor is easier to compute? I feel the usefulness has dropped quite a lot since the time of Ising, who had no observation capability at the atomic size.

 

Present research is on spintronics, with ferromagnetic semiconductors.

[timo]

I assume you meant a random-field Ising model rather than an Ising model (whose ground state is trivial in 2+ dimensions). I'm not particularly familiar with ground state calculations in this model. But maybe this paper, the only one related to your question I ever encountered, is a start (although probably not undergrad level): http://arxiv.org/pdf/1010.5973

 

@Enthalpy: While admittedly much of modern science is "observe a model no one observed before", "create an experimental setup no one could make previously" or "make a computer simulation larger or more detailed than any before" some science still is about finding basic principles why a system behaves like it does. In statistical physics, some work into this direction is devoted to categorizing systems into so-called universality classes. Systems belonging to the same class are supposed to have similar behavior in some respect, irrespective of their microscopic details. Hence, when it comes to studying the universal behavior of a system, the Ising model and its variations are still being investigated (e.g. http://arxiv.org/pdf/1008.3299).

Edited October 4, 2013 by timo