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Title: | Spin glass phase transition on scale-free networks |
Authors: | Kim, DH Kahng, B Rodgers, GJ Kim, D |
Keywords: | Spin glasses;Ising model;Ferromagnetic-paramagnetic transitions;Magnetisation;Critical exponents |
Issue Date: | 2006 |
Publisher: | American Physical Society |
Citation: | Physical review E 71: 056115, Aug 2006 |
Abstract: | We study the Ising spin-glass model on scale-free networks generated by the static model using the replica method. Based on the replica-symmetric solution, we derive the phase diagram consisting of the paramagnetic (P), ferromagnetic (F), and spin glass (SG) phases as well as the Almeida-Thouless line as functions of the degree exponent , the mean degree K, and the fraction of ferromagnetic interactions r. To reflect the inhomogeneity of vertices, we modify the magnetization m and the spin-glass order parameter q with vertex- weights. The transition temperature Tc (Tg) between the P-F (P-SG) phases and the critical behaviors of the order parameters are found analytically. When 2<<3, Tc and Tg are infinite, and the system is in the F phase or the mixed phase for r>1/2, while it is in the SG phase at r=1/2. m and q decay as power-laws with increasing temperature with different -dependent exponents. When >3, the Tc and Tg are finite and related to the percolation threshold. The critical exponents associated with m and q depend on for 3<<5 (3<<4) at the P-F (P-SG) boundary |
URI: | http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PLEEE8000071000005056115000001&idtype=cvips&gifs=yes http://bura.brunel.ac.uk/handle/2438/287 |
Appears in Collections: | Mathematical Physics Dept of Mathematics Research Papers Mathematical Sciences |
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