A 0/1 spin Ising model on Barabasi-Albert networks shows first-order transitions and hysteresis, but reduces by the authors' own variable transformation to a classical Ising model with local fields.
Exact Solution of Ising Model on a Small-World Network
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abstract
We present an exact solution of a one-dimensional Ising chain with both nearest neighbor and random long-range interactions. Not surprisingly, the solution confirms the mean field character of the transition. This solution also predicts the finite-size scaling that we observe in numerical simulations.
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A Modified Ising Model of Barab\'asi-Albert Network with Gene-type Spins
A 0/1 spin Ising model on Barabasi-Albert networks shows first-order transitions and hysteresis, but reduces by the authors' own variable transformation to a classical Ising model with local fields.