Nature of the spin-glass phase in dense packings of Ising dipoles with random anisotropy axes

Abstract

Using tempered Monte Carlo simulations, we study the the spin-glass phase of dense packings of Ising dipoles pointing along random axes. We consider systems of dipoles (i) placed on the sites of a simple cubic lattice with lattice constant d, and (ii) placed at the center of random close packed spheres of diameter d that occupy 64% of the volume. For both cases, we find a spin-glass phase below a certain temperature T . By analysing the data obtained for the overlap parameter, the associated correlation length, as well as the statistics of the overlap distributions of individual samples, we find a behavior consistent with quasi-long-range order in the spin-glass phase, similar to the one previously found in strongly diluted dipolar systems.

Phase diagram for ensembles of random close-packed Ising-like dipoles as a function of texturation

“…A similar SG phase has been previously found for other dipolar systems with strong frozen disorder, namely for systems of parallel Ising dipoles with strong dilution as well as in dense arrays, both crystalline of not, of nontextured systems of Ising dipoles with the axes oriented completely at random. 17,44 However, given the moderate range of system sizes considered here, our data cannot rule out completely the so-called replica symmetry breaking scenario in which q 2 does not vanish in the N → ∞ limit, but there are long range SG order fluctuations which provoke B q < 1. 42,43 C. The FM-SG transition.…”

“…The results agree well with the limiting value T sg = 0.8 found in previous work for the RAD case (σ = ∞). 17 It is important to stress that the fact that the B q curves cross at T sg does not imply the existence of strong longrange order for T < T sg . 39 Indeed, plots of B q vs 1/L for T ≤ T sg (σ) show that B q stays below 1 (see the inset in Fig.…”

“…16 An equilibrium SG phase for non-textured RCP ensembles of dipolar spheres has recently been found by numerical simulations. 17 Nevertheless, the role of positional and orientational disorder in non-crystalline ensembles is far from being completely understood. Numerical simulations have shown that frozen amorphous densely packed systems with volume fractions as high as φ = 0.42 order ferromagnetically provided they are textured.…”

“…The thermal equilibration times t 0 are assessed by the same procedure of Ref. 17 . The overlap q(t) of configurations created from two replicas of the same sample J are obtained by evolving the replicas independently after having started from random configurations.…”

“…31 In the simulations we have examined the ±q symmetry of the overlap distributions p J (q) as an additional indication that all samples are well thermalized. 17 A double average, the thermal one for each sample J and the above-mentioned average over the N s samples, is needed to achieve physical results. The first average is taken within the time interval [t 0 , 2t 0 ].…”