%0 Journal Article %1 WOS:000264767400013 %A Andrade, R F S %A Jr., J S Andrade %A Herrmann, H J %C ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA %D 2009 %I AMER PHYSICAL SOC %J PHYSICAL REVIEW E %K Ising magnetic magnetisation; model; networks; properties} susceptibility; thermodynamic transitions; {complex %N 3, 2 %R 10.1103/PhysRevE.79.036105 %T Ising model on the Apollonian network with node-dependent interactions %V 79 %X This work considers an Ising model on the Apollonian network, where the exchange constant J(i,j)similar to 1/(k(i)k(j))(mu) between two neighboring spins (i,j) is a function of the degree k of both spins. Using the exact geometrical construction rule for the network, the thermodynamical and magnetic properties are evaluated by iterating a system of discrete maps that allows for very precise results in the thermodynamic limit. The results can be compared to the predictions of a general framework for spin models on scale-free networks, where the node distribution P(k)similar to k(-gamma), with node-dependent interacting constants. We observe that, by increasing mu, the critical behavior of the model changes from a phase transition at T=infinity for a uniform system (mu=0) to a T=0 phase transition when mu=1: in the thermodynamic limit, the system shows no true critical behavior at a finite temperature for the whole mu >= 0 interval. The magnetization and magnetic susceptibility are found to present noncritical scaling properties.

@article{WOS:000264767400013, abstract = {This work considers an Ising model on the Apollonian network, where the exchange constant J(i,j)similar to 1/(k(i)k(j))(mu) between two neighboring spins (i,j) is a function of the degree k of both spins. Using the exact geometrical construction rule for the network, the thermodynamical and magnetic properties are evaluated by iterating a system of discrete maps that allows for very precise results in the thermodynamic limit. The results can be compared to the predictions of a general framework for spin models on scale-free networks, where the node distribution P(k)similar to k(-gamma), with node-dependent interacting constants. We observe that, by increasing mu, the critical behavior of the model changes from a phase transition at T=infinity for a uniform system (mu=0) to a T=0 phase transition when mu=1: in the thermodynamic limit, the system shows no true critical behavior at a finite temperature for the whole mu >= 0 interval. The magnetization and magnetic susceptibility are found to present noncritical scaling properties.}, added-at = {2022-05-23T20:00:14.000+0200}, address = {ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA}, author = {Andrade, R F S and Jr., J S Andrade and Herrmann, H J}, biburl = {https://www.bibsonomy.org/bibtex/24f3380dda35fdc19434599c33d392103/ppgfis_ufc_br}, doi = {10.1103/PhysRevE.79.036105}, interhash = {69642877d92910c8df4806f71f81934f}, intrahash = {4f3380dda35fdc19434599c33d392103}, issn = {1539-3755}, journal = {PHYSICAL REVIEW E}, keywords = {Ising magnetic magnetisation; model; networks; properties} susceptibility; thermodynamic transitions; {complex}, number = {3, 2}, publisher = {AMER PHYSICAL SOC}, pubstate = {published}, timestamp = {2022-05-23T20:00:14.000+0200}, title = {Ising model on the Apollonian network with node-dependent interactions}, tppubtype = {article}, volume = 79, year = 2009 }