Boolean decision problems with competing interactions on scalefree networks: Critical thermodynamics
Abstract
We study the critical behavior of Boolean variables on scalefree networks with competing interactions (Ising spin glasses). Our analytical results for the disordernetworkdecayexponent phase diagram are verified using Monte Carlo simulations. When the probability of positive (ferromagnetic) and negative (antiferromagnetic) interactions is the same, the system undergoes a finitetemperature spinglass transition if the exponent that describes the decay of the interaction degree in the scalefree graph is strictly larger than 3. However, when the exponent is equal to or less than 3, a spinglass phase is stable for all temperatures. The robustness of both the ferromagnetic and spinglass phases suggests that Boolean decision problems on scalefree networks are quite stable to local perturbations. Finally, we show that for a given decay exponent spin glasses on scalefree networks seem to obey universality. Furthermore, when the decay exponent of the interaction degree is larger than 4 in the spinglass sector, the universality class is the same as for the meanfield SherringtonKirkpatrick Ising spin glass.
 Publication:

Physical Review E
 Pub Date:
 September 2012
 DOI:
 10.1103/PhysRevE.86.031116
 arXiv:
 arXiv:1202.1153
 Bibcode:
 2012PhRvE..86c1116K
 Keywords:

 75.50.Lk;
 75.40.Mg;
 05.50.+q;
 64.60.i;
 Spin glasses and other random magnets;
 Numerical simulation studies;
 Lattice theory and statistics;
 General studies of phase transitions;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 14 pages, lots of figures and 2 tables