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.
%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
}