Title: Thermodynamics of spin systems on small-world hypergraphs
Authors: Bollé, Désiré ×
Heylen, Rob
Skantzos, N. S #
Issue Date: Nov-2006
Publisher: Published by the American Physical Society through the American Institute of Physics
Series Title: Physical Review E, Statistical, Nonlinear and Soft Matter Physics vol:74 issue:5
Article number: 056111
Abstract: We study the thermodynamic properties of spin systems on small-world hypergraphs, obtained by superimposing sparse Poisson random graphs with p-spin interactions onto a one-dimensional Ising chain with nearest-neighbor interactions. We use replica-symmetric transfer-matrix techniques to derive a set of fixed-point equations describing the relevant order parameters and free energy, and solve them employing population dynamics. In the special case where the number of connections per site is of the order of the system size, we are able to solve the model analytically. In the more general case where the number of connections is finite, we determine the static and dynamic ferromagnetic-paramagnetic transitions using population dynamics. The results are tested against Monte-Carlo simulations.
ISSN: 1539-3755
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Theoretical Physics Section
× corresponding author
# (joint) last author

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