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

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 ⟨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 RF = √ 2/πJ. 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.

Glassy Behaviour of Random Field on Bethe Lattice in an External Magnetic Field

“…. This result agrees with those obtained by [35,36]. Because they found that a finite external field removes sharp phase transitions by…”

“…The maximum of the peak lowers with increasing B. This result agrees with that obtained by Bannora et al [36] as well as agrees with that obtained by Ismail [37]. He found that real and imaginary parts of the dynamic susceptibility display maxima at C T T = .…”