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Register a new userEffective Spin-1/2 Description of Transverse-Field-Induced Random Fields in Dipolar Spin Glasses with Strong Single-Ion Anisotropy
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We present analytical and numerical evidence for the validity of an effective S=1/2 approach to the description of random field generation in S>=1, and especially in an S=1, dipolar spin glass models with strong uniaxial Ising anisotropy and subject to weak external magnetic field Bx transverse to the Ising direction. Explicitely Bx-dependent random fields are shown to naturally emerge in the effective low-energy description of a microscopic S=1 toy model. We discuss our results in relation to recent theoretical studies pertaining to the topic of Bx-induced random fields in the LiHo$_x$Y$_{1-x}$F$_4$ magnetic materials with the Ho$^{3+}$ Ising moments subject to a transverse field. We show that the S_{eff}=1/2 approach is able to capture both the qualitative and quantitative aspects of the physics at small Bx, giving results that agree with those obtained using conventional second order perturbation theory.
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Numerical results for the local field distributions of a family of Ising spin-glass models are presented. In particular, the Edwards-Anderson model in dimensions two, three, and four is considered, as well as spin glasses with long-range power-law-modulated interactions that interpolate between a nearest-neighbour Edwards-Anderson system in one dimension and the infinite-range Sherrington-Kirkpatrick model. Remarkably, the local field distributions only depend weakly on the range of the interactions and the dimensionality, and show strong similarities except for near zero local field.
We consider the paramagnetic phase of the random transverse-field Ising spin chain and study the dynamical properties by numerical methods and scaling considerations. We extend our previous work [Phys. Rev. B 57, 11404 (1998)] to new quantities, such as the non-linear susceptibility, higher excitations and the energy-density autocorrelation function. We show that in the Griffiths phase all the above quantities exhibit power-law singularities and the corresponding critical exponents, which vary with the distance from the critical point, can be related to the dynamical exponent z, the latter being the positive root of [(J/h)^{1/z}]_av=1. Particularly, whereas the average spin autocorrelation function in imaginary time decays as [G]_av(t)~t^{-1/z}, the average energy-density autocorrelations decay with another exponent as [G^e]_av(t)~t^{-2-1/z}.
We study chaotic size dependence of the low temperature correlations in the SK spin glass. We prove that as temperature scales to zero with volume, for any typical coupling realization, the correlations cycle through every spin configuration in every fixed observation window. This cannot happen in short-ranged models as there it would mean that every spin configuration is an infinite-volume ground state. Its occurrence in the SK model means that the commonly used `modified clustering notion of states sheds little light on the RSB solution of SK, and conversely, the RSB solution sheds little light on the thermodynamic structure of EA models.
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.
We study magnetic properties of spin glass SG systems under a random field (RF), beased on the suggestion that RFs can be induced by a weak transverse field in the compound LiHo$_x$Y$_{1-x}$F$_4$. We consider a cluster spin model that allows long-range disordered interactions among clusters and short-range interactions inside the clusters, besides a local RF for each spin following a Gaussian distribution with standard deviation $Delta$. We adopt the one-step replica symmetry breaking (RSB) approach to get an exactly solvable single-cluster problem. We discuss the behavior of order parameters, specific heat $C_{m}$, nonlinear susceptibility $chi_3$ and phase diagrams for different disorder configurations. In the absence of RF, the $chi_3$ exhibits a divergence at $T_f$, while the $C_{m}$ shows a broad maximum at a temperature $T^{**}$ around 30$%$ above $T_f$, as expected for conventional SG systems. The presence of RF changes this scenario. The $C_{m}$ still shows the maximum at $T^{**}$ that is weakly dependent on $Delta$. However, the $T_f$ is displaced to lower temperatures, enhancing considerable the ration $T^{**}/T_f$. Furthermore, the divergence in $chi_3$ is replaced by a rounded maximum at a temperature $T^{*}$, which becomes increasingly higher than $T_f$ as $Delta$ enhances. As a consequence, the paramagnetic phase is unfolded in three regions: (i) a conventional paramagnetism ($T>T^{**}$; (ii) a region with formation of short-range order with frozen spins ($T^{*}<T<T^{**}$); (iii) a region with slow growth of free-energy barriers slowing down the spin dynamics before the SG transition ($T_f<T<T^{*}$) suggesting an intermediate Griffiths phase before the SG state. Our results reproduce qualitatively some findings of LiHo$_x$Y$_{1-x}$F$_4$ as the rounded maximum of $chi_3$ behavior triggered by RF.
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