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Chin. Phys. B, 2010, Vol. 19(10): 107501    DOI: 10.1088/1674-1056/19/10/107501

Glassy phase and thermodynamics for random field Ising model on spherical lattice in magnetic field

Galal Ismaila, Wafaa Hassana, Khalid Bannorab
a Mathematics and Physics Department, Faculty of Engineering, Port Said Branch of Suez Canal University, Port Said, Egypt; b Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt
Abstract  Phase diagram and thermodynamic parameters of the random field Ising model (RFIM) on spherical lattice are studied by using mean field theory. This lattice is placed in an external magnetic field (B). The random field (hi) is assumed to be Gaussian distributed with zero mean and a variance < hi2 > = HRF2 . The free energy (F), the magnetization (M) and the order parameter (q) are calculated. The ferromagnetic (FM) spin-glass (SG) phase transition is clearly observed. The critical temperature (TC) is computed under a critical intensity of random field . The phase transition from FM to paramagnetic (PM) occurs at TC = J / k in the absence of magnetic field. The critical temperature decreases as HRF increases in the phase boundary of FM-to-SG. The magnetic susceptibility (χ) shows a sharp cusp at TC and the specific heat (C) has a singularity in small random field. The internal energy (U) has a similar behaviour to that obtained from the Monte Carlo simulation.
Keywords:  random field      mean field theory      magnetization      specific heat and phase diagram     
Received:  18 October 2009      Published:  15 October 2010
PACS:  75.10.Hk (Classical spin models)  
  75.10.Nr (Spin-glass and other random models)  
  75.30.Cr (Saturation moments and magnetic susceptibilities)  
  75.30.Kz (Magnetic phase boundaries (including classical and quantum magnetic transitions, metamagnetism, etc.))  
  75.40.Cx (Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.))  
  75.60.Ej (Magnetization curves, hysteresis, Barkhausen and related effects)  

Cite this article: 

Khalid Bannora, Galal Ismail, Wafaa Hassan Glassy phase and thermodynamics for random field Ising model on spherical lattice in magnetic field 2010 Chin. Phys. B 19 107501

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