XY model in small-world networks.

The phase transition in the XY model on one-dimensional small-world networks is investigated by means of Monte Carlo simulations. It is found that long-range order is present at finite temperatures, even for very small values of the rewiring probability, suggesting a finite-temperature transition for any nonzero rewiring probability. Nature of the phase transition is discussed in comparison with the globally coupled XY model.

[1]  Moshe Gitterman,et al.  Small-world phenomena in physics: the Ising model , 2000 .

[2]  M. Newman,et al.  Renormalization Group Analysis of the Small-World Network Model , 1999, cond-mat/9903357.

[3]  S. Ruffo,et al.  Clustering and relaxation in Hamiltonian long-range dynamics. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  D S Callaway,et al.  Network robustness and fragility: percolation on random graphs. , 2000, Physical review letters.

[5]  M. Newman,et al.  Exact solution of site and bond percolation on small-world networks. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  M. Newman,et al.  Epidemics and percolation in small-world networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  M. D. Menezes,et al.  First-order transition in small-world networks , 1999, cond-mat/9903426.

[8]  A. Komives,et al.  Shape of the 8B alpha and neutrino spectra. , 2000, Physical review letters.

[9]  L F Lago-Fernández,et al.  Fast response and temporal coherent oscillations in small-world networks. , 1999, Physical review letters.

[10]  M. Newman,et al.  Scaling and percolation in the small-world network model. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  M. Weigt,et al.  On the properties of small-world network models , 1999, cond-mat/9903411.

[12]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[13]  L. Amaral,et al.  Small-World Networks: Evidence for a Crossover Picture , 1999, cond-mat/9903108.

[14]  Mark Newman,et al.  Models of the Small World , 2000 .

[15]  M. Kuperman,et al.  Small world effect in an epidemiological model. , 2000, Physical review letters.

[16]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[17]  D. Thouless,et al.  Ordering, metastability and phase transitions in two-dimensional systems , 1973 .

[18]  R. Botet,et al.  Size Scaling for Infinitely Coordinated Systems , 1982 .

[19]  M E Newman,et al.  Scientific collaboration networks. I. Network construction and fundamental results. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  M. Ožana.  Incipient spanning cluster on small-world networks , 2001 .

[21]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[22]  L. Amaral,et al.  Erratum: Small-World Networks: Evidence for a Crossover Picture [Phys. Rev. Lett. 82, 3180 (1999)] , 1999, cond-mat/9906247.

[23]  D. Thouless,et al.  Long range order and metastability in two dimensional solids and superfluids. (Application of dislocation theory) , 1972 .

[24]  M. Newman,et al.  Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.