Thermodynamics of spin systems on small-world hypergraphs

Details Thermodynamics of spin systems on small-world hypergraphs Thermodynamics of spin systems on small-world hypergraphs

2006-05-22

arxiv.org/abs/cond-mat/0605527v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

14 pages, 7 figures; Added 2 figures. Extended results

Scientific paper

10.1103/PhysRevE.74.056111

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.

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