3 research outputs found
Random field Ising systems on a general hierarchical lattice: Rigorous inequalities
Random Ising systems on a general hierarchical lattice with both, random
fields and random bonds, are considered. Rigorous inequalities between
eigenvalues of the Jacobian renormalization matrix at the pure fixed point are
obtained. These inequalities lead to upper bounds on the crossover exponents
.Comment: LaTeX, 13 pages, figs. 1a,1b,2. To be published in PR
The stabilizing role of itinerant ferromagnetism in inter-granular cohesion in iron
We present a simple, general energy functional for ferromagnetic materials
based upon a local spin density extension to the Stoner theory of itinerant
ferromagnetism. The functional reproduces well available ab initio results and
experimental interfacial energies for grain boundaries in iron. The model shows
that inter-granular cohesion along symmetric tilt boundaries in iron is
dependent upon strong magnetic structure at the interface, illuminates the
mechanisms underlying this structure, and provides a simple explanation for
relaxation of the atomic structure at these boundaries.Comment: In review at Phys. Rev. Lett. Submitted 23 September 1997; revised 16
March 199
Full reduction of large finite random Ising systems by RSRG
We describe how to evaluate approximately various physical interesting
quantities in random Ising systems by direct renormalization of a finite
system. The renormalization procedure is used to reduce the number of degrees
of freedom to a number that is small enough, enabling direct summing over the
surviving spins. This procedure can be used to obtain averages of functions of
the surviving spins. We show how to evaluate averages that involve spins that
do not survive the renormalization procedure. We show, for the random field
Ising model, how to obtain the "connected" 2-spin correlation function and the
"disconnected" 2-spin correlation function. Consequently, we show how to obtain
the average susceptibility and the average energy. For an Ising system with
random bonds and random fields we show how to obtain the average specific heat.
We conclude by presenting our numerical results for the average susceptibility
and the "connected" 2-spin correlation function along one of the principal
axes. (We believe this to be the first time, where the full three dimensional
correlation is calculated and not just parameters like Nu or Eta.) The results
for the average susceptibility are used to extract the critical temperature and
critical exponents of the 3D random field Ising system.Comment: 30 pages, 17 figure