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- Lee, Sang Hoon, 1982-, et al.
(författare)
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Critical behavior of the Ising model in annealed scale-free networks
- 2009
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1063-651X .- 1095-3787. ; 80:051127
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Tidskriftsartikel (refereegranskat)abstract
- We study the critical behavior of the Ising model in annealed scale-free (SF) networks of finite system size with forced upper cutoff in degree. By mapping the model onto the weighted fully connected Ising model, we derive analytic results for the finite-size scaling (FSS) near the phase transition, characterized by the cutoff-dependent two-parameter scaling with four distinct scaling regimes, in highly heterogeneous networks. These results are essentially the same as those found for the nonequilibrium contact process in annealed SF networks, except for an additional complication due to the trivial critical point shift in finite systems. The discrepancy of the FSS theories between annealed and quenched SF networks still remains in the equilibrium Ising model, like some other nonequilibrium models. All of our analytic results are confirmed reasonably well by numerical simulations.
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| 2. |
- Lee, Sang Hoon, 1982-, et al.
(författare)
-
Random field Ising model on networks with inhomogeneous connections
- 2006
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1063-651X .- 1095-3787. ; 74:031118
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Tidskriftsartikel (refereegranskat)abstract
- We study a zero-temperature phase transition in the random field Ising model on scale-free networks with the degree exponent γ. Using an analytic mean-field theory, we find that the spins are always in the ordered phase for γ<3. On the other hand, the spins undergo a phase transition from an ordered phase to a disordered phase as the dispersion of the random fields increases for γ>3. The phase transition may be either continuous or discontinuous depending on the shape of the random field distribution. We derive the condition for the nature of the phase transition. Numerical simulations are performed to confirm the results.
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