Dynamics and termination cost of spatially coupled meanfield models
Abstract
This work is motivated by recent progress in information theory and signal processing where the socalled spatially coupled design of systems leads to considerably better performance. We address relevant open questions about spatially coupled systems through the study of a simple Ising model. In particular, we consider a chain of CurieWeiss models that are coupled by interactions up to a certain range. Indeed, it is well known that the pure (uncoupled) CurieWeiss model undergoes a firstorder phase transition driven by the magnetic field, and furthermore in the spinodal region such systems are unable to reach equilibrium in subexponential time if initialized in the metastable state. In contrast, the spatially coupled system is instead able to reach the equilibrium even when initialized to the metastable state. The equilibrium phase propagates along the chain in the form of a traveling wave. Here we study the speed of the wave front and the socalled termination cost—i.e., the conditions necessary for the propagation to occur. We reach several interesting conclusions about optimization of the speed and the cost.
 Publication:

Physical Review E
 Pub Date:
 January 2014
 DOI:
 10.1103/PhysRevE.89.012102
 arXiv:
 arXiv:1310.2121
 Bibcode:
 2014PhRvE..89a2102C
 Keywords:

 05.70.Fh;
 89.20.Ff;
 02.50.Tt;
 Phase transitions: general studies;
 Computer science and technology;
 Inference methods;
 Condensed Matter  Statistical Mechanics;
 Computer Science  Information Theory
 EPrint:
 12 pages, 11 figures