Boolean decision problems with competing interactions on scalefree networks: Equilibrium and nonequilibrium behavior in an external bias
Abstract
We study the equilibrium and nonequilibrium properties of Boolean decision problems with competing interactions on scalefree networks in an external bias (magnetic field). Previous studies at zero field have shown a remarkable equilibrium stability of Boolean variables (Ising spins) with competing interactions (spin glasses) on scalefree networks. When the exponent that describes the powerlaw decay of the connectivity of the network is strictly larger than 3, the system undergoes a spinglass transition. However, when the exponent is equal to or less than 3, the glass phase is stable for all temperatures. First, we perform finitetemperature Monte Carlo simulations in a field to test the robustness of the spinglass phase and show that the system has a spinglass phase in a field, i.e., exhibits a de AlmeidaThouless line. Furthermore, we study avalanche distributions when the system is driven by a field at zero temperature to test if the system displays selforganized criticality. Numerical results suggest that avalanches (damage) can spread across the whole system with nonzero probability when the decay exponent of the interaction degree is less than or equal to 2, i.e., that Boolean decision problems on scalefree networks with competing interactions can be fragile when not in thermal equilibrium.
 Publication:

Physical Review E
 Pub Date:
 February 2014
 DOI:
 10.1103/PhysRevE.89.022118
 arXiv:
 arXiv:1310.1139
 Bibcode:
 2014PhRvE..89b2118Z
 Keywords:

 05.50.+q;
 75.50.Lk;
 75.40.Mg;
 64.60.i;
 Lattice theory and statistics;
 Spin glasses and other random magnets;
 Numerical simulation studies;
 General studies of phase transitions;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 14 pages, 10 figures