Rounding of firstorder phase transitions and optimal cooperation in scalefree networks
Abstract
We consider the ferromagnetic large q state Potts model in complex evolving networks, which is equivalent to an optimal cooperation problem, in which the agents try to optimize the total sum of pair cooperation benefits and the supports of independent projects. The agents are found to be typically of two kinds: A fraction of m (being the magnetization of the Potts model) belongs to a large cooperating cluster, whereas the others are isolated one man’s projects. It is shown rigorously that the homogeneous model has a strongly firstorder phase transition, which turns to secondorder for random interactions (benefits), the properties of which are studied numerically on the BarabásiAlbert network. The distribution of finitesize transition points is characterized by a shift exponent, 1/ν∼^{'}=0.26(1) , and by a different width exponent, 1/ν^{'}=0.18(1) , whereas the magnetization at the transition point scales with the size of the network, N , as m∼N^{x} , with x=0.66(1) .
 Publication:

Physical Review E
 Pub Date:
 October 2007
 DOI:
 10.1103/PhysRevE.76.041107
 arXiv:
 arXiv:0704.1538
 Bibcode:
 2007PhRvE..76d1107K
 Keywords:

 05.50.+q;
 64.60.Fr;
 75.10.Nr;
 Lattice theory and statistics;
 Equilibrium properties near critical points critical exponents;
 Spinglass and other random models;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks;
 Physics  Physics and Society
 EPrint:
 8 pages, 6 figures