Small-World Network Effect in Competing Glauber- and Kawasaki-type Dynamics

TL;DR

This paper explores how small-world network effects influence competing Glauber- and Kawasaki-type dynamics within the Gaussian model, revealing phase diagram modifications and distinct impacts on each dynamic process.

Contribution

It introduces analysis of small-world network effects on competing Glauber- and Kawasaki-type dynamics, highlighting their different influences on phase behavior and system organization.

Findings

Small-world effects alter phase diagrams significantly.

Glauber dynamics are influenced mainly by average coordination number.

Kawasaki dynamics are enhanced by long-range interactions.

Abstract

In this article, we investigate the competing Glauber-type and Kawasaki-type dynamics with small-world network (SWN) effect, in the framework of the Gaussian model. The Glauber-type single-spin transition mechanism with probability p simulates the contact of the system with a heat bath and the Kawasaki-type dynamics with probability 1-p simulates an external energy flux. Two different types of SWN effect are studied, one with the total number of links increased and the other with it conserved. The competition of the dynamics leads to an interesting self-organization process that can be characterized by a phase diagram with two identifiable temperatures. By studying the modification of the phase diagrams, the SWN effect on the two dynamics is analyzed. For the Glauber-type dynamics, more important is the altered average coordination number while the Kawasaki-type dynamics is enhanced by the long range spin interaction and redistribution.