Monte Carlo study of the spin-glass phase of the site-diluted dipolar Ising model

By tempered Monte Carlo simulations, we study site-diluted Ising systems of magnetic dipoles. All dipoles are randomly placed on a fraction x of all L^3 sites of a simple cubic lattice, and point along a given crystalline axis. For x_c< x<=1, where x_c = 0.65, we find an antiferromagnetic phase below a temperature which vanishes as x tends to x_c from above. At lower values of x, we find an equilibrium spin-glass (SG) phase below a temperature given by k_B T_{sg} = x e_d, where e_d is a nearest neighbor dipole-dipole interaction energy. We study (a) the relative mean square deviation D_q^2 of |q|, where q is the SG overlap parameter, and (b) xi_L/L, where xi_L is a correlation length. From their variation with temperature and system size, we determine T_{sg}. In the SG phase, we find (i) the mean values and decrease algebraically with L as L increases, (ii) double peaked, but wide, distributions of q/ appear to be independent of L, and (iii) xi_L/L rises with L at constant T, but extrapolations to 1/L -> 0 give finite values. All of this is consistent with quasi-long-range order in the SG phase.Comment: 15 LaTeX pages, 15 figures, 3 tables. (typos fixed in Appendix A

Reply to Comment on "Magnetization Process of Single Molecule Magnets at Low Temperatures"

This is the reply to a Comment by I.S.Tupitsyn and P.C.E. Stamp (PRL v92,119701 (2004)) on a letter of ours (J.F.Fernandez and J.J.Alonso, PRL v91, 047202 (2003)).Comment: 2 LaTeX pages, 1 eps figure. Submitted to PRL on 20 October 200

Time relaxation of interacting single--molecule magnets

We study the relaxation of interacting single--molecule magnets (SMMs) in both spatially ordered and disordered systems. The tunneling window is assumed to be, as in Fe8, much narrower than the dipolar field spread. We show that relaxation in disordered systems differs qualitatively from relaxation in fully occupied cubic and Fe_8 lattices. We also study how line shapes that develop in ''hole--digging'' experiments evolve with time t in these fully occupied lattices. We show (1) that the dipolar field h scales as t^p in these hole line shapes and show (2) how p varies with lattice structure. Line shapes are not, in general, Lorentzian. More specifically, in the lower portion of the hole, they behave as (h/t^p)^{(1/p)-1} if h is outside the tunnel window. This is in agreement with experiment and with our own Monte Carlo results.Comment: 21 LaTeX pages, 6 eps figures. Submitted to PRB on 15 June 2005. Accepted on 13 August 200

The group of strong Galois objects associated to a cocommutative Hopf quasigroup

Let H be a cocommutative faithfully flat Hopf quasigroup in a strict symmetric monoidal category with equalizers. In this paper we introduce the notion of (strong) Galois H-object and we prove that the set of isomorphism classes of (strong) Galois H-objects is a (group) monoid which coincides, in the Hopf algebra setting, with the Galois group of H-Galois objects introduced by Chase and Sweedler