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

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=\sqrt2/\piJ. 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.