On the discontinuity of the specific heat of the Ising model on a scale-free network

Abstract

We consider the Ising model on an annealed scale-free network with node-degree distribution characterized by a power-law decay P(K)∼ K^{-λ}. It is well established that the model is characterized by classical mean-field exponents for λ > 5. In this note we show that the specific-heat discontinuity δc_{h} at the critical point remains λ-dependent even for λ > 5: δc_{h}=3(λ-5)(λ-1)/[2(λ-3)^2] and attains its mean-field value δc_{h}=3/2 only in the limit λ → ∞. We compare this behaviour with recent measurements of the d dependency of δc_{h} made for the Ising model on lattices with d > 4 [Lundow P.H., Markström K., Nucl. Phys. B, 2015, 895, 305].

Keywords

• Ising model
• scale-free networks
• annealed network