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Glassy behaviour of random field Ising spins on Bethe lattice in external magnetic field |
| Khalid Bannoraa), Galal Ismaila)†, and Wafaa Hassanb) |
| a Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt; b Mathematics and Physics Department, Faculty of Engineering, Port Said Branch of Suez, Canal University, Port Said, Egypt |
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Abstract The thermodynamics and the phase diagram of random field Ising model (RFIM) on Bethe lattice are studied by using a replica trick. This lattice is placed in an external magnetic field ($B$). A Gaussian distribution of random field $( {h_{\rm i} } )$ with zero mean and variance $\langle {{h}_{\rm i}^{\rm 2} } \rangle = { H}_{{\rm RF}}^{\rm 2} $ is considered. The free-energy ($F$), the magnetization ($M$) and the order parameter ($q$) are investigated for several values of coordination number ($z$). The phase diagram shows several interesting behaviours and presents tricritical point at critical temperature $T_{\rm C} = J / k$ and when $H_{\rm RF} = 0$ for finite $z$. The free-energy ($F$) values increase as $T$ increases for different intensities of random field ($H_{\rm RF} $) and finite $z$. The internal energy ($U$) has a similar behaviour to that obtained from the Monte Carlo simulations. The ground state of magnetization decreases as the intensity of random field $H_{\rm RF} $ increases. The ferromagnetic (FM)--paramagnetic (PM) phase boundary is clearly observed only when $z \to \infty $. While FM--PM-spin glass (SG) phase boundaries are present for finite $z$. The magnetic susceptibility ($\chi $) shows a sharp cusp at $T_{\rm C} $ in a small random field for finite $z$ and rounded different peaks on increasing $H_{\rm RF}$.
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Received: 25 September 2010
Revised: 25 December 2010
Accepted manuscript online:
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PACS:
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75.10.Nr
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(Spin-glass and other random models)
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75.40.B
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76.20.+q
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(General theory of resonances and relaxations)
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Cite this article:
Khalid Bannora, Galal Ismail, and Wafaa Hassan Glassy behaviour of random field Ising spins on Bethe lattice in external magnetic field 2011 Chin. Phys. B 20 067501
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