Ising critical exponents on random trees and graphs

S. Dommers, C. Giardina, R.W. Hofstad, van der

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We study the critical behavior of the ferromagnetic Ising model on random trees as well as so-called locally tree-like random graphs. We pay special attention to trees and graphs with a power-law offspring or degree distribution whose tail behavior is characterized by its power-law exponent t > 2. We show that the critical inverse temperature of the Ising model equals the inverse hyperbolic tangent of the inverse of the mean offspring or mean forward degree distribution. In particular, the critical inverse temperature equals zero when t ¿ (2,3] where this mean equals infinity. We further study the critical exponents d, ß and ¿, describing how the (root) magnetization behaves close to criticality. We rigorously identify these critical exponents and show that they take the values as predicted by Dorogovstev, et al. [12] and Leone et al. [23]. These values depend on the power-law exponent t taking the mean-field values for t > 5, but different values for t ¿ (3,5).
Originele taal-2Engels
Plaats van productieEindhoven
UitgeverijEurandom
Aantal pagina's39
StatusGepubliceerd - 2013

Publicatie series

NaamReport Eurandom
Volume2013025
ISSN van geprinte versie1389-2355

Vingerafdruk

Random Trees
Random Graphs
Ising
Critical Exponents
Degree Distribution
Inverse hyperbolic tangent
Ising Model
Power Law
Exponent
Tail Behavior
Power-law Distribution
Criticality
Critical Behavior
Magnetization
Mean Field
Infinity
Roots
Zero
Graph in graph theory

Citeer dit

Dommers, S., Giardina, C., & Hofstad, van der, R. W. (2013). Ising critical exponents on random trees and graphs. (Report Eurandom; Vol. 2013025). Eindhoven: Eurandom.
Dommers, S. ; Giardina, C. ; Hofstad, van der, R.W. / Ising critical exponents on random trees and graphs. Eindhoven : Eurandom, 2013. 39 blz. (Report Eurandom).
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Dommers, S, Giardina, C & Hofstad, van der, RW 2013, Ising critical exponents on random trees and graphs. Report Eurandom, vol. 2013025, Eurandom, Eindhoven.

Ising critical exponents on random trees and graphs. / Dommers, S.; Giardina, C.; Hofstad, van der, R.W.

Eindhoven : Eurandom, 2013. 39 blz. (Report Eurandom; Vol. 2013025).

Onderzoeksoutput: Boek/rapportRapportAcademic

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Dommers S, Giardina C, Hofstad, van der RW. Ising critical exponents on random trees and graphs. Eindhoven: Eurandom, 2013. 39 blz. (Report Eurandom).