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