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We study the kinetics of domain growth in ferromagnets with random exchange interactions. We present detailed Monte Carlo results for the nonconserved random-bond Ising model, which are consistent with power-law growth with a variable exponent. These results are interpreted in the context of disorder barriers with a logarithmic dependence on the domain size. Further, we clarify the implications of logarithmic barriers for both nonconserved and conserved domain growth.
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We reconsider the problem of the critical behavior of a three-dimensional $O(m)$ symmetric magnetic system in the presence of random anisotropy disorder with a generic trimodal random axis distribution. By introducing $n$ replicas to average over disorder it can be coarse-grained to a $phi^{4}$-theory with $m times n$ component order parameter and five coupling constants taken in the limit of $n to 0$. Using a field theory approach we renormalize the model to two-loop order and calculate the $beta$-functions within the $varepsilon$ expansion and directly in three dimensions. We analyze the corresponding renormalization group flows with the help of the Pade-Borel resummation technique. We show that there is no stable fixed point accessible from physical initial conditions whose existence was argued in the previous studies. This may indicate an absence of a long-range ordered phase in the presence of random anisotropy disorder with a generic random axis distribution.
The random dipolar magnet LiHo$_x$Y$_{1-x}$F$_4$ enters a strongly frustrated regime for small Ho$^{3+}$ concentrations with $x<0.05$. In this regime, the magnetic moments of the Ho$^{3+}$ ions experience small quantum corrections to the common Ising approximation of LiHo$_x$Y$_{1-x}$F$_4$, which lead to a $Z_2$-symmetry breaking and small, degeneracy breaking energy shifts between different eigenstates. Here we show that destructive interference between two almost degenerate excitation pathways burns spectral holes in the magnetic susceptibility of strongly driven magnetic moments in LiHo$_x$Y$_{1-x}$F$_4$. Such spectral holes in the susceptibility, microscopically described in terms of Fano resonances, can already occur in setups of only two or three frustrated moments, for which the driven level scheme has the paradigmatic $Lambda$-shape. For larger clusters of magnetic moments, the corresponding level schemes separate into almost isolated many-body $Lambda$-schemes, in the sense that either the transition matrix elements between them are negligibly small or the energy difference of the transitions is strongly off-resonant to the drive. This enables the observation of Fano resonances, caused by many-body quantum corrections to the common Ising approximation also in the thermodynamic limit. We discuss its dependence on the driving strength and frequency as well as the crucial role that is played by lattice dissipation.
We investigate thermodynamic phase transitions of the joint presence of spin glass (SG) and random field (RF) using a random graph model that allows us to deal with the quenched disorder. Therefore, the connectivity becomes a controllable parameter in our theory, allowing us to answer what the differences are between this description and the mean-field theory i.e., the fully connected theory. We have considered the random network random field Ising model where the spin exchange interaction as well as the RF are random variables following a Gaussian distribution. The results were found within the replica symmetric (RS) approximation, whose stability is obtained using the two-replica method. This also puts our work in the context of a broader discussion, which is the RS stability as a function of the connectivity. In particular, our results show that for small connectivity there is a region at zero temperature where the RS solution remains stable above a given value of the magnetic field no matter the strength of RF. Consequently, our results show important differences with the crossover between the RF and SG regimes predicted by the fully connected theory.
The fidelity susceptibility measures sensitivity of eigenstates to a change of an external parameter. It has been fruitfully used to pin down quantum phase transitions when applied to ground states (with extensions to thermal states). Here we propose to use the fidelity susceptibility as a useful dimensionless measure for complex quantum systems. We find analytically the fidelity susceptibility distributions for Gaussian orthogonal and unitary universality classes for arbitrary system size. The results are verified by a comparison with numerical data.
We study numerically the depinning transition of driven elastic interfaces in a random-periodic medium with localized periodic-correlation peaks in the direction of motion. The analysis of the moving interface geometry reveals the existence of several characteristic lengths separating different length-scale regimes of roughness. We determine the scaling behavior of these lengths as a function of the velocity, temperature, driving force, and transverse periodicity. A dynamical roughness diagram is thus obtained which contains, at small length scales, the critical and fast-flow regimes typical of the random-manifold (or domain wall) depinning, and at large length-scales, the critical and fast-flow regimes typical of the random-periodic (or charge-density wave) depinning. From the study of the equilibrium geometry we are also able to infer the roughness diagram in the creep regime, extending the depinning roughness diagram below threshold. Our results are relevant for understanding the geometry at depinning of arrays of elastically coupled thin manifolds in a disordered medium such as driven particle chains or vortex-line planar arrays. They also allow to properly control the effect of transverse periodic boundary conditions in large-scale simulations of driven disordered interfaces.
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