Phase diagram of the Ising Model on a Cayley tree in the presence of competing interactions and magnetic field |
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Authors: | Ananias M Mariz Constantino Tsallis E L Albuquerque |
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Institution: | (1) Centro Brasileiro de Pesquisas Fisicas/CNPq, Rua Dr. Xavier Sigaud, 150, 22290 Rio de Janeiro, RJ, Brazil;(2) Departamento de Fisica, Universidade Federal do Rio Grande do Norte, 5900 Natal, RN, Brazil |
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Abstract: | We study the phase diagram for the Ising Model on a Cayley tree with competing nearest-neighbor interactionsJ
1 and next-nearest-neighbor interactionsJ
2 andJ
3 in the presence of an external magnetic field. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers, as particular cases, previous works by Vannimenus and by Inawashiroet al. At vanishing temperature, the phase diagram is fully determined, for all values and signs ofJ
2/J
1 andJ
3/J
2; in particular, we verify that values ofJ
3/J
2 high enough favor the paramagnetic phase. At finite temperatures, several interesting features (evolution of reentrances, separation of the modulated region into two disconnected pieces, etc.) are exhibited for typical values ofJ
2/J
1 andJ
3/J
2.Partially supported by the Brazilian Agencies CNPq and FINEP. |
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Keywords: | Ising model Cayley tree devil's staircase spin-glass |
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