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Register a new userEquilibrium spin-glass transition of magnetic dipoles with random anisotropy axes on a site diluted lattice
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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|.
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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.
We study by Monte Carlo simulations the effect of quenched orientational disorder in systems of interacting classical dipoles on a square lattice. Each dipole can lie along any of two perpendicular axes that form an angle psi with the principal axes of the lattice. We choose psi at random and without bias from the interval [-Delta, Delta] for each site of the lattice. For 0<Delta <~ pi/4 we find a thermally driven second order transition between a paramagnetic and a dipolar antiferromagnetic order phase and critical exponents that change continously with Delta. Near the case of maximum disorder Delta ~ pi/4 we still find a second order transition at a finite temperature T_c but our results point to weak instead of {it strong} long-ranged dipolar order for temperatures below T_c.
Using Monte Carlo simulations, we study the character of the spin-glass (SG) state of a site-diluted dipolar Ising model. We consider systems of dipoles randomly placed on a fraction x of all L^3 sites of a simple cubic lattice that point up or down along a given crystalline axis. For x < 0.65 these systems are known to exhibit an equilibrium spin-glass phase below a temperature T_sg proportional to x. At high dilution and very low temperatures, well deep in the SG phase, we find spiky distributions of the overlap parameter q that are strongly sample-dependent. We focus on spikes associated with large excitations. From cumulative distributions of q and a pair correlation function averaged over several thousands of samples we find that, for the system sizes studied, the average width of spikes, and the fraction of samples with spikes higher than a certain threshold does not vary appreciably with L. This is compared with the behaviour found for the Sherrington-Kirkpatrick model.
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.
We develop a novel method based in the sparse random graph to account the interplay between geometric frustration and disorder in cluster magnetism. Our theory allows to introduce the cluster network connectivity as a controllable parameter. Two types of inner cluster geometry are considered: triangular and tetrahedral. The theory was developed for a general, non-uniform intra-cluster interactions, but in the present paper the results presented correspond to uniform, anti-ferromagnetic (AF) intra-clusters interactions $J_{0}/J$. The clusters are represented by nodes on a finite connectivity random graph, and the inter-cluster interactions are random Gaussian distributed. The graph realizations are treated in replica theory using the formalism of order parameter functions, which allows to calculate the distribution of local fields and, as a consequence, the relevant observable. In the case of triangular cluster geometry, there is the onset of a classical Spin Liquid state at a temperature $T^{*}/J$ and then, a Cluster Spin Glass (CSG) phase at a temperature $T_{f}/J$. The CSG ground state is robust even for very weak disorder or large negative $J_{0}/J$. These results does not depend on the network connectivity. Nevertheless, variations in the connectivity strongly affect the level of frustration $f_{p}=-Theta_{CW}/T_{f}$ for large $J_{0}/J$. In contrast, for the non-frustrated tetrahedral cluster geometry, the CSG ground state is suppressed for weak disorder or large negative $J_{0}/J$. The CSG boundary phase presents a re-entrance which is dependent on the network connectivity.
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