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

The thermodynamics of random field Ising model (RFIM) on Bethe lattice is
studied by using the replica trick (Bethe lattice is placed in an external
magnetic field (B)). A Gaussian distribution for random field with variance
2
RF
2
i h = H is considered. The free-energy (F), magnetization (M), order
parameter (q), susceptibility ( χ ) and internal energy (U) are calculated. The
phase diagram is investigated at different values of co-ordination number
z = 3,4,5,6 and z → ∞ . The phase diagram shows several interesting
behaviours and present tricritical point at critical
temperatureT J k c = / , = 0 RF H for finite co-ordination number (z). The
critical temperature ( c T ) and the corresponding value of RF H are found.
Finally, we compare our results with the recent results obtained before for spins
glasses.