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Statistical mechanics of complex networks
 Rev. Mod. Phys
"... Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as ra ..."
Abstract

Cited by 1202 (8 self)
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Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real
Thermodynamic versus Topological Phase Transitions: Cusp in the Kertész Line
, 2008
"... We present a study of phase transitions of the mean–field Potts model at (inverse) temperature β, in presence of an external field h. Both thermodynamic and topological aspects of these transitions are considered. For the first aspect we complement previous results and give an explicit equation of ..."
Abstract

Cited by 1 (1 self)
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We present a study of phase transitions of the mean–field Potts model at (inverse) temperature β, in presence of an external field h. Both thermodynamic and topological aspects of these transitions are considered. For the first aspect we complement previous results and give an explicit equation of the thermodynamic transition line in the β–h plane as well as the magnitude of the jump of the magnetization (for q � 3). The signature of the latter aspect is characterized here by the presence or not of a giant component in the clusters of a Fortuin–Kasteleyn type representation of the model. We give the equation of the Kertész line separating (in the β–h plane) the two behaviours. As a result, we get that this line exhibits, as soon as q � 3, a very interesting cusp where it separates from the thermodynamic transition line.