Rigidity percolation in a field

Details Rigidity percolation in a field Rigidity percolation in a field

2003-06-13

arxiv.org/abs/cond-mat/0306380v2

Phys.Rev. E68 (2003) 056104

Physics

Condensed Matter

Statistical Mechanics

RevTeX4, psfig, 16 pages. Equation numbering corrected. Minor typos corrected

Scientific paper

10.1103/PhysRevE.68.056104

Rigidity Percolation with g degrees of freedom per site is analyzed on randomly diluted Erdos-Renyi graphs with average connectivity gamma, in the presence of a field h. In the (gamma,h) plane, the rigid and flexible phases are separated by a line of first-order transitions whose location is determined exactly. This line ends at a critical point with classical critical exponents. Analytic expressions are given for the densities n_f of uncanceled degrees of freedom and gamma_r of redundant bonds. Upon crossing the coexistence line, n_f and gamma_r are continuous, although their first derivatives are discontinuous. We extend, for the case of nonzero field, a recently proposed hypothesis, namely that the density of uncanceled degrees of freedom is a ``free energy'' for Rigidity Percolation. Analytic expressions are obtained for the energy, entropy, and specific heat. Some analogies with a liquid-vapor transition are discussed. Particularizing to zero field, we find that the existence of a (g+1)-core is a necessary condition for rigidity percolation with g degrees of freedom. At the transition point gamma_c, Maxwell counting of degrees of freedom is exact on the rigid cluster and on the (g+1)-rigid-core, i.e. the average coordination of these subgraphs is exactly 2g, although gamma_r, the average coordination of the whole system, is smaller than 2g. gamma_c is found to converge to 2g for large g, i.e. in this limit Maxwell counting is exact globally as well. This paper is dedicated to Dietrich Stauffer, on the occasion of his 60th birthday.

Affiliated with

Also associated with

No associations

Rating

Rigidity percolation in a field 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 Rigidity percolation in a field, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rigidity percolation in a field will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-26384