Title: On the discontinuity of the specific heat of the Ising model on a scale-free network
Author(s):

	M. Krasnytska ( Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii St., 79011 Lviv, Ukraine; Institut Jean Lamour, Université de Lorraine, F-54506 Vandœuvre les Nancy, France; Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry (L4)),
	B. Berche (Institut Jean Lamour, Université de Lorraine, F-54506 Vandœ uvre les Nancy, France ;Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry (L4)),
	Yu. Holovatch ( Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii St., 79011 Lviv, Ukraine; Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry (L4)),
	R. Kenna ( Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, United Kingdom; Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry (L4))

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].

Key words: Ising model, scale-free networks, annealed network
PACS: 64.60.aq, 64.60.fd, 64.70.qd, 64.60.De

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