Condensed Matter Physics, 2015, vol. 18, No. 4, 44601
DOI:10.5488/CMP.18.44601
arXiv:1510.06216
Title:
On the discontinuity of the specific heat of the Ising model on a scalefree 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, F54506 Vandœuvre les Nancy, France;
Doctoral College for the Statistical Physics of Complex Systems, LeipzigLorraineLvivCoventry (L^{4})),


B. Berche
(Institut Jean Lamour, Université de Lorraine, F54506 Vandœ uvre les Nancy, France ;Doctoral College for the Statistical Physics of Complex Systems,
LeipzigLorraineLvivCoventry (L^{4})),


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, LeipzigLorraineLvivCoventry (L^{4})),


R. Kenna
( Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, United Kingdom;
Doctoral College for the Statistical Physics of Complex Systems, LeipzigLorraineLvivCoventry (L^{4}))

We consider the Ising model on an annealed scalefree network with nodedegree distribution characterized by a powerlaw decay P(K)∼ K^{λ}.
It is well established that the model is characterized by classical meanfield exponents for λ > 5.
In this note we show that the specificheat discontinuity δc_h at the critical point remains λdependent
even for λ > 5: δc_{h}=3(λ5)(λ1)/[2(λ3)^2] and attains its meanfield 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, scalefree networks, annealed network
PACS:
64.60.aq, 64.60.fd, 64.70.qd, 64.60.De
