Scaling properties of the critical behavior in the dilute antiferromagnet Fe(0.93)Zn(0.07)F2

Critical scattering analyses for dilute antiferromagnets are made difficult by the lack of predicted theoretical line shapes beyond mean-field models. Nevertheless, with the use of some general scaling assumptions we have developed a procedure by which we can analyze the equilibrium critical scattering in these systems for H=0, the random-exchange Ising model, and, more importantly, for H>0, the random-field Ising model. Our new fitting approach, as opposed to the more conventional techniques, allows us to obtain the universal critical behavior exponents and amplitude ratios as well as the critical line shapes. We discuss the technique as applied to Fe(0.93)Zn(0.07)F2. The general technique, however, should be applicable to other problems where the scattering line shapes are not well understood but scaling is expected to hold.Comment: 17 pages, 5 figure

Computer simulation of the critical behavior of 3D disordered Ising model

The critical behavior of the disordered ferromagnetic Ising model is studied numerically by the Monte Carlo method in a wide range of variation of concentration of nonmagnetic impurity atoms. The temperature dependences of correlation length and magnetic susceptibility are determined for samples with various spin concentrations and various linear sizes. The finite-size scaling technique is used for obtaining scaling functions for these quantities, which exhibit a universal behavior in the critical region; the critical temperatures and static critical exponents are also determined using scaling corrections. On the basis of variation of the scaling functions and values of critical exponents upon a change in the concentration, the conclusion is drawn concerning the existence of two universal classes of the critical behavior of the diluted Ising model with different characteristics for weakly and strongly disordered systems.Comment: 14 RevTeX pages, 6 figure

Ground state numerical study of the three-dimensional random field Ising model

The random field Ising model in three dimensions with Gaussian random fields is studied at zero temperature for system sizes up to 60^3. For each realization of the normalized random fields, the strength of the random field, Delta and a uniform external, H is adjusted to find the finite-size critical point. The finite-size critical point is identified as the point in the H-Delta plane where three degenerate ground states have the largest discontinuities in the magnetization. The discontinuities in the magnetization and bond energy between these ground states are used to calculate the magnetization and specific heat critical exponents and both exponents are found to be near zero.Comment: 10 pages, 6 figures; new references and small changes to tex

On the nature of the phase transition in the three-dimensional random field Ising model

A brief survey of the theoretical, numerical and experimental studies of the random field Ising model during last three decades is given. Nature of the phase transition in the three-dimensional RFIM with Gaussian random fields is discussed. Using simple scaling arguments it is shown that if the strength of the random fields is not too small (bigger than a certain threshold value) the finite temperature phase transition in this system is equivalent to the low-temperature order-disorder transition which takes place at variations of the strength of the random fields. Detailed study of the zero-temperature phase transition in terms of simple probabilistic arguments and modified mean-field approach (which take into account nearest-neighbors spin-spin correlations) is given. It is shown that if all thermally activated processes are suppressed the ferromagnetic order parameter m(h) as the function of the strength $h$ of the random fields becomes history dependent. In particular, the behavior of the magnetization curves m(h) for increasing and for decreasing $h$ reveals the hysteresis loop.Comment: 22 pages, 12 figure

Ordering in the dilute weakly-anisotropic antiferromagnet Mn(0.35)Zn(0.65)F2

The highly diluted antiferromagnet Mn(0.35)Zn(0.65)F2 has been investigated by neutron scattering in zero field. The Bragg peaks observed below the Neel temperature TN (approximately 10.9 K) indicate stable antiferromagnetic long-range ordering at low temperature. The critical behavior is governed by random-exchange Ising model critical exponents (nu approximately 0.69 and gamma approximately 1.31), as reported for Mn(x)Zn(1-x)F2 with higher x and for the isostructural compound Fe(x)Zn(1-x)F2. However, in addition to the Bragg peaks, unusual scattering behavior appears for |q|>0 below a glassy temperature Tg approximately 7.0 K. The glassy region T<Tg corresponds to that of noticeable frequency dependence in earlier zero-field ac susceptibility measurements on this sample. These results indicate that long-range order coexists with short-range nonequilibrium clusters in this highly diluted magnet.Comment: 7 pages, 5 figure

Random-field critical scattering at high magnetic concentration in the Ising antiferromagnet Fe{sub 0.93}Zn{sub 0.07}F{sub 2}

The high magnetic concentration ising antiferromagnet Fe{sub 0.93}Zn{sub 0.07}F{sub 2} does not exhibit the severe critical scattering hysteresis at low temperatures observed in all lower concentration samples studied. The system therefore provides equilibrium neutron scattering line shapes suitable for determining random-field Ising model critical behavior