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Register a new userMagnetic ordering of random dense packings of freely rotating dipoles
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We study random dense packings of Heisenberg dipoles by numerical simulation. The dipoles are at the centers of identical spheres that occupy fixed random positions in space and fill a fraction $Phi$ of the spatial volume. The parameter $Phi$ ranges from rather low values, typical of amorphous ensembles, to the maximum $Phi$=0.64 that occurs in the random-close-packed limit. We assume that the dipoles can freely rotate and have no local anisotropies. As well as the usual thermodynamical variables, the physics of such systems depends on $Phi$. Concretely, we explore the magnetic ordering of these systems in order to depict the phase diagram in the temperature-$Phi$ plane. For $Phi gtrsim0.49$ we find quasi-long-range ferromagnetic order coexisting with strong long-range spin-glass order. For $Phi lesssim0.49$ the ferromagnetic order disappears giving way to a spin-glass phase similar to the ones found for Ising dipolar systems with strong frozen disorder.
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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 L^3 dipoles (a) placed on the sites of a simple cubic lattice with lattice constant $d$, (b) placed at the center of randomly closed packed spheres of diameter d that occupy a 64% of the volume. For both cases we find an equilibrium spin-glass phase below a temperature T_sg. We compute the spin-glass overlap parameter q and their associated correlation length xi_L. From the variation of xi_L with T and L we determine T_sg for both systems. In the spin-glass phase, we find (a) <q> decreases algebraically with L, and (b) xi_L/L does not diverge as L increases. At very low temperatures we find comb-like distributions of q that are sample-dependent. We find that the fraction of samples with cross-overlap spikes higher than a certain value as well as the average width of the spikes are size independent quantities. All these results are consistent with a quasi-long-range order in the spin-glass phase, as found previously for very diluted dipolar systems.
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We study partially occupied lattice systems of classical magnetic dipoles which point along randomly oriented axes. Only dipolar interactions are taken into account. The aim of the model is to mimic collective effects in disordered assemblies of magnetic nanoparticles. From tempered Monte Carlo simulations, we obtain the following equilibrium results. The zero temperature entropy approximately vanishes. Below a temperature T_c, given by k_B T_c= (0.95 +- 0.1)x e_d, where e_d is a nearest neighbor dipole-dipole interaction energy and x is the site occupancy rate, we find a spin glass phase. In it, (1) the mean value <|q|>, where q is the spin overlap, decreases algebraically with system size N as N increases, and (2) D|q| = 0.5 <|q|> (T/x)^1/2, independently of N, where D|q| is the root mean square deviation of |q|.
We study the ordering statistics of 4 random walkers on the line, obtaining a much improved estimate for the long-time decay exponent of the probability that a particle leads to time $t$; $P_{rm lead}(t)sim t^{-0.91287850}$, and that a particle lags to time $t$ (never assumes the lead); $P_{rm lag}(t)sim t^{-0.30763604}$. Exponents of several other ordering statistics for $N=4$ walkers are obtained to 8 digits accuracy as well. The subtle correlations between $n$ walkers that lag {em jointly}, out of a field of $N$, are discussed: For $N=3$ there are no correlations and $P_{rm lead}(t)sim P_{rm lag}(t)^2$. In contrast, our results rule out the possibility that $P_{rm lead}(t)sim P_{rm lag}(t)^3$ for $N=4$, though the correlations in this borderline case are tiny.
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