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

doi:10.1088/1674-1056/19/10/107501

中国物理B ›› 2010, Vol. 19 ›› Issue (10): 107501-107501.doi: 10.1088/1674-1056/19/10/107501

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

Galal Ismail¹, Wafaa Hassan¹, Khalid Bannora²

(1)Mathematics and Physics Department, Faculty of Engineering, Port Said Branch of Suez Canal University, Port Said, Egypt; (2)Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt

收稿日期:2009-10-18 修回日期:2010-03-04 出版日期:2010-10-15 发布日期:2010-10-15

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

Khalid Bannora^a), Galal Ismail^a)†, and Wafaa Hassan^b)

^a Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt; ^bMathematics and Physics Department, Faculty of Engineering, Port Said Branch of Suez Canal University, Port Said, Egypt

Received:2009-10-18 Revised:2010-03-04 Online:2010-10-15 Published:2010-10-15

摘要/Abstract

摘要： 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 (h_i) is assumed to be Gaussian distributed with zero mean and a variance < h_i² > = H_RF² . 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 (T_C) is computed under a critical intensity of random field . The phase transition from FM to paramagnetic (PM) occurs at T_C = J / k in the absence of magnetic field. The critical temperature decreases as H_RF increases in the phase boundary of FM-to-SG. The magnetic susceptibility (χ) shows a sharp cusp at T_C 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.

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 (h_i) is assumed to be Gaussian distributed with zero mean and a variance < h_i² > = H_RF² . 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 (T_C) is computed under a critical intensity of random field $H_{\rm RF}=\sqrt{2/\pi}J$. The phase transition from FM to paramagnetic (PM) occurs at T_C = J / k in the absence of magnetic field. The critical temperature decreases as H_RF increases in the phase boundary of FM-to-SG. The magnetic susceptibility ($\chi$) shows a sharp cusp at T_C 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.

Key words: random field, mean field theory, magnetization, specific heat and phase diagram

中图分类号: (Classical spin models)

75.10.Hk

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)

Khalid Bannora, Galal Ismail, Wafaa Hassan. Glassy phase and thermodynamics for random field Ising model on spherical lattice in magnetic field[J]. 中国物理B, 2010, 19(10): 107501-107501.

Khalid Bannora, Galal Ismail, and Wafaa Hassan. Glassy phase and thermodynamics for random field Ising model on spherical lattice in magnetic field[J]. Chin. Phys. B, 2010, 19(10): 107501-107501.

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

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

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