First-order transition in small-world networks
Instituto de Física, Universidade Federal Fluminense CEP
24210-340, Niterói, RJ, Brazil
Accepted: 25 March 2000
The small-world transition is a first-order transition at zero density p of shortcuts, whereby the normalised shortest-path distance undergoes a discontinuity in the thermodynamic limit. On finite systems the apparent transition is shifted by . Equivalently a “persistence size” can be defined in connection with finite-size effects. Assuming , simple rescaling arguments imply that . We confirm this result by extensive numerical simulation in one to four dimensions, and argue that implies that this transition is first order.
PACS: 05.10.-a – Computational methods in statistical physics and nonlinear dynamics / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 64.60.-i – General studies of phase transitions
© EDP Sciences, 2000