Chains of Mean Field Models

Computer Science – Discrete Mathematics

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

We consider a collection of Curie-Weiss (CW) spin systems, possibly with a random field, each of which is placed along the positions of a one-dimensional chain. The CW systems are coupled together by a Kac-type interaction in the longitudinal direction of the chain and by an infinite range interaction in the direction transverse to the chain. Our motivations for studying this model come from recent findings in the theory of error correcting codes based on spatially coupled graphs. We find that, although much simpler than the codes, the model studied here already displays similar behaviors. We are interested in the van der Waals curve in a regime where the size of each Curie-Weiss model tends to infinity, and the length of the chain and range of the Kac interaction are large but finite. Below the critical temperature, and with appropriate boundary conditions, there appears a series of equilibrium states representing kink-like interfaces between the two equilibrium states of the individual system. The van der Waals curve oscillates periodically around the Maxwell plateau. These oscillations have a period inversely proportional to the chain length and an amplitude exponentially small in the range of the interaction; in other words the spinodal points of the chain model lie exponentially close to the phase transition threshold. The amplitude of the oscillations is closely related to a Peierls-Nabarro free energy barrier for the motion of the kink along the chain. Analogies to similar phenomena and their possible algorithmic significance for graphical models of interest in coding theory and theoretical computer science are pointed out.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Chains of Mean Field Models 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 Chains of Mean Field Models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Chains of Mean Field Models will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-689494

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.