No Arabic abstract
URh_2Ge_2 occupies an extraordinary position among the heavy-electron 122-compounds, by exhibiting a previously unidentified form of magnetic correlations at low temperatures, instead of the usual antiferromagnetism. Here we present new results of ac and dc susceptibilities, specific heat and neutron diffraction on single-crystalline as-grown URh_2Ge_2. These data clearly indicate that crystallographic disorder on a local scale produces spin glass behavior in the sample. We therefore conclude that URh_2Ge_2 is a 3D Ising-like, random-bond, heavy-fermion spin glass.
The interplay between quantum fluctuations and disorder is investigated in a spin-glass model, in the presence of a uniform transverse field $Gamma$, and a longitudinal random field following a Gaussian distribution with width $Delta$. The model is studied through the replica formalism. This study is motivated by experimental investigations on the LiHo$_x$Y$_{1-x}$F$_4$ compound, where the application of a transverse magnetic field yields rather intriguing effects, particularly related to the behavior of the nonlinear magnetic susceptibility $chi_3$, which have led to a considerable experimental and theoretical debate. We analyzed two situations, namely, $Delta$ and $Gamma$ considered as independent, as well as these two quantities related as proposed recently by some authors. In both cases, a spin-glass phase transition is found at a temperature $T_f$; moreover, $T_f$ decreases by increasing $Gamma$ towards a quantum critical point at zero temperature. The situation where $Delta$ and $Gamma$ are related appears to reproduce better the experimental observations on the LiHo$_x$Y$_{1-x}$F$_4$ compound, with the theoretical results coinciding qualitatively with measurements of the nonlinear susceptibility. In this later case, by increasing $Gamma$, $chi_3$ becomes progressively rounded, presenting a maximum at a temperature $T^*$ ($T^*>T_f$). Moreover, we also show that the random field is the main responsible for the smearing of the nonlinear susceptibility, acting significantly inside the paramagnetic phase, leading to two regimes delimited by the temperature $T^*$, one for $T_f<T<T^*$, and another one for $T>T^*$. It is argued that the conventional paramagnetic state corresponds to $T>T^*$, whereas the temperature region $T_f<T<T^*$ may be characterized by a rather unusual dynamics, possibly including Griffiths singularities.
Machine learning-inspired techniques have emerged as a new paradigm for analysis of phase transitions in quantum matter. In this work, we introduce a supervised learning algorithm for studying critical phenomena from measurement data, which is based on iteratively training convolutional networks of increasing complexity, and test it on the transverse field Ising chain and q=6 Potts model. At the continuous Ising transition, we identify scaling behavior in the classification accuracy, from which we infer a characteristic classification length scale. It displays a power-law divergence at the critical point, with a scaling exponent that matches with the diverging correlation length. Our algorithm correctly identifies the thermodynamic phase of the system and extracts scaling behavior from projective measurements, independently of the basis in which the measurements are performed. Furthermore, we show the classification length scale is absent for the $q=6$ Potts model, which has a first order transition and thus lacks a divergent correlation length. The main intuition underlying our finding is that, for measurement patches of sizes smaller than the correlation length, the system appears to be at the critical point, and therefore the algorithm cannot identify the phase from which the data was drawn.
We numerically investigate the structure of many-body wave functions of 1D random quantum circuits with local measurements employing the participation entropies. The leading term in system size dependence of participation entropies indicates a multifractal scaling of the wave-functions at any non-zero measurement rate. The sub-leading term contains universal information about measurement--induced phase transitions and plays the role of an order parameter, being non-zero in the error-correcting phase and vanishing in the quantum Zeno phase. We provide an analytical interpretation of this behavior expressing the participation entropy in terms of partition functions of classical statistical models in 2D.
We investigate the generalized p-spin models that contain arbitrary diagonal operators U with no reflection symmetry. We derive general equations that give an opportunity to uncover the behavior of the system near the glass transition at different (continuous) p. The quadrupole glass with J=1 is considered as an illustrating example. It is shown that the crossover from continuous to discontinuous glass transition to one-step replica breaking solution takes place at p=3.3 for this model. For p <2+Delta p, where Delta p= 0.5 is a finite value, stable 1RSB-solution disappears. This behaviour is strongly different from that of the p-spin Ising glass model.
Magnetic ordering at low temperature for Ising ferromagnets manifests itself within the associated Fortuin-Kasteleyn (FK) random cluster representation as the occurrence of a single positive density percolating network. In this paper we investigate the percolation signature for Ising spin glass ordering -- both in short-range (EA) and infinite-range (SK) models -- within a two-replica FK representation and also within the different Chayes-Machta-Redner two-replica graphical representation. Based on numerical studies of the $pm J$ EA model in three dimensions and on rigorous results for the SK model, we conclude that the spin glass transition corresponds to the appearance of {it two} percolating clusters of {it unequal} densities.