Reference : Random matrix models for phase diagrams
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Physics
http://hdl.handle.net/2268/90327
Random matrix models for phase diagrams
English
Vanderheyden, Benoît mailto [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Electronique et microsystèmes >]
Jackson, A. D. [The Niels Bohr International Academy, Blegdamsvej 17, DK-2100 Copenhagen, Denmark > > > >]
2011
Reports on Progress in Physics
Institute of Physics
74
102001
Yes (verified by ORBi)
International
0034-4885
1361-6633
London
United Kingdom
[en] We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from QCD to high-T_c materials. Instead of working from specific models, phase diagrams are constructed by averaging over the ensemble of theories that possesses the relevant symmetries of the problem. Although approximate in nature, this approach has a number of advantages. First, it can be useful in distinguishing generic features from model-dependent details. Second, it can help in understanding the `minimal' number of symmetry constraints required to reproduce specific phase structures. Third, the robustness of predictions can be checked with respect to variations in the detailed description of the interactions. Finally, near critical points, random matrix models bear strong similarities to Ginsburg-Landau theories with the advantage of additional constraints inherited from the symmetries of the underlying interaction. These constraints can be helpful in ruling out certain topologies in the phase diagram. In this Key Issue, we illustrate the basic structure of random matrix models, discuss their strengths and weaknesses, and consider the kinds of system to which they can be applied.
http://hdl.handle.net/2268/90327
http://stacks.iop.org/0034-4885/74/102001
Please cite as:
Rep. Prog. Phys. 74 (2011) 102001.

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