Replicated Transfer Matrix Analysis of Ising Spin Models on `Small World' Lattices

Details Replicated Transfer Matrix Analysis of Ising Spin Models on `Small World' Lattices Replicated Transfer Matrix Analysis of Ising Spin Models on `Small World' Lattices

2004-02-19

arxiv.org/abs/cond-mat/0402504v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

22 pages, LaTeX, IOP macros, eps figures

Scientific paper

10.1088/0305-4470/37/25/003

We calculate equilibrium solutions for Ising spin models on `small world' lattices, which are constructed by super-imposing random and sparse Poissonian graphs with finite average connectivity c onto a one-dimensional ring. The nearest neighbour bonds along the ring are ferromagnetic, whereas those corresponding to the Poisonnian graph are allowed to be random. Our models thus generally contain quenched connectivity and bond disorder. Within the replica formalism, calculating the disorder-averaged free energy requires the diagonalization of replicated transfer matrices. In addition to developing the general replica symmetric theory, we derive phase diagrams and calculate effective field distributions for two specific cases: that of uniform sparse long-range bonds (i.e. `small world' magnets), and that of (+J/-J) random sparse long-range bonds (i.e. `small world' spin-glasses).

Affiliated with

Also associated with

No associations

Rating

Replicated Transfer Matrix Analysis of Ising Spin Models on `Small World' Lattices 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 Replicated Transfer Matrix Analysis of Ising Spin Models on `Small World' Lattices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Replicated Transfer Matrix Analysis of Ising Spin Models on `Small World' Lattices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-213957