Majority rule dynamics in finite dimensions.

We investigate the long-time behavior of a majority rule opinion dynamics model in finite spatial dimensions. Each site of the system is endowed with a two-state spin variable that evolves by majority rule. In a single update event, a group of spins with a fixed (odd) size is specified and all members of the group adopt the local majority state. Repeated application of this update step leads to a coarsening mosaic of spin domains and ultimate consensus in a finite system. The approach to consensus is governed by two disparate time scales, with the longer time scale arising from realizations in which spins organize into coherent single-opinion bands. The consequences of this geometrical organization on the long-time kinetics are explored.

[1]  R. Glauber.  Time‐Dependent Statistics of the Ising Model , 1963 .

[2]  S. Redner,et al.  Fate of zero-temperature Ising ferromagnets. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  F. Slanina,et al.  Analytical results for the Sznajd model of opinion formation , 2003, cond-mat/0305102.

[4]  A. Bray.  Theory of phase-ordering kinetics , 1994, cond-mat/9501089.

[5]  S. Redner.  A guide to first-passage processes , 2001 .

[6]  A. Barabasi,et al.  Fractal concepts in surface growth , 1995 .

[7]  S. Galam.  Application of statistical physics to politics , 1999, cond-mat/0004306.

[8]  Sidney Redner,et al.  A guide to first-passage processes , 2001 .

[9]  Krapivsky.  Kinetics of monomer-monomer surface catalytic reactions. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[10]  S Redner,et al.  Freezing in Ising ferromagnets. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Liu,et al.  Time-reversal invariance and universality of two-dimensional growth models. , 1987, Physical review. B, Condensed matter.

[12]  S. Redner,et al.  Dynamics of majority rule in two-state interacting spin systems. , 2003, Physical review letters.

[13]  A. Soulier,et al.  The dynamics of multidimensional secession: fixed points and ideological condensation. , 2003, Physical review letters.

[14]  A. Barabasi,et al.  Fractal Concepts in Surface Growth: Frontmatter , 1995 .

[15]  Katarzyna Sznajd-Weron,et al.  Opinion evolution in closed community , 2000, cond-mat/0101130.