Effective field theory for models defined over small-world networks. First and second order phase transitions

Details Effective field theory for models defined over small-world networks. First and second order phase transitions Effective field theory for models defined over small-world networks. First and second order phase transitions

2008-09-03

arxiv.org/abs/0809.0606v1

Phys. Rev. E 78, 031102 (2008)

Physics

Condensed Matter

Disordered Systems and Neural Networks

28 pages, 18 figures; merged version of the manuscripts arXiv:0801.3454 and arXiv:0801.3563 conform to the published version

Scientific paper

10.1103/PhysRevE.78.031102

We present an effective field theory method to analyze, in a very general way, models defined over small-world networks. Even if the exactness of the method is limited to the paramagnetic regions and to some special limits, it provides, yielding a clear and immediate (also in terms of calculation) physical insight, the exact critical behavior and the exact critical surfaces and percolation thresholds. The underlying structure of the non random part of the model, i.e., the set of spins filling up a given lattice L_0 of dimension d_0 and interacting through a fixed coupling J_0, is exactly taken into account. When J_0\geq 0, the small-world effect gives rise, as is known, to a second-order phase transition that takes place independently of the dimension d_0 and of the added random connectivity c. When J_0<0, a different and novel scenario emerges in which, besides a spin glass transition, multiple first- and second-order phase transitions may take place. As immediate analytical applications we analyze the Viana-Bray model (d_0=0), the one dimensional chain (d_0=1), and the spherical model for arbitrary d_0.

Affiliated with

Also associated with

No associations

Rating

Effective field theory for models defined over small-world networks. First and second order phase transitions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Effective field theory for models defined over small-world networks. First and second order phase transitions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Effective field theory for models defined over small-world networks. First and second order phase transitions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-104606