The probability distributions analyzed were discrete, for random exchange interactions and/or random magnetic fields [8]. In the identification of the RFIM with diluted antiferromagnets in the presence of a uniform magnetic field, the local random fields are expressed in terms of quantities that vary in both signal and magnitude [4, 5]. (7). approached. This discussion is based on quenched random-field models, but an extension to the case of nonequilibrium diluted antiferromagnets was discussed by some authors [8, 18]. At low temperatures, increased frustration favors the spin-glass phase (before it disappears) over the ferromagnetic phase and symmetrically the antiferromagnetic phase. 'Closed Form Approximations for Lattice Systems', by D.M. 6 (upper figure, left side) the susceptibility as a function of the temperature only for the size L=128. Hemmer and J.L. A. P. Young and H. G. Katzgraber, Phys. Voronel. to other lattices, higher dimensions and quantum phase transitions. In this study, we have analysed in detail the critical and tricritical properties of thermodynamic Ricci curvature scalar for a quantum lattice system with the local three-well potentials in the presence of the external pressure. The new fixed point has complex eigenvalues, leading to oscillating corrections to scaling, and has a correlation-length exponent ν=2/a. From the above FSS forms, Eqs. 0000013651 00000 n A. Haroni and C. E. Paraskevaidis, Phys. Due to these motivations, we have studied the NRFIM on a square lattice with nearest-neighbors interactions and in the presence of random magnetic fields that follow a double-gaussian probability distribution. 0000008476 00000 n Rev. thus governed by the criterion $\nu > 2/3$ rather than the usual Harris Watson. and discusses some possible directions for future research. Emch. The researchers find their results very promising. Lett. Khorzhenko. irrelevant and the rare-region classification which predicts unconventional Course LIX. Griffiths singularities [Phys. That is, one may assume that spins and impurities (or fields) behave more independently of each other than in the annealed model so that a conflict occurs, and a steady nonequilibrium condition prevails asymptotically. 'Exactly Solvable Models for Many-Body Systems Far from Equilibrium', by G.M. 'The Large-n Limit in Statistical Mechanics and the Spectral Theory of Disordered Systems', by A.M. Khorunzhy, B.A. In Fig. Thompson. 0000011206 00000 n Our random lattice data provide strong evidence that, for the available system sizes, the resulting effective critical exponents are indistinguishable from recent high-precision estimates obtained in Monte Carlo studies of the Ising model and φ4 field theory on three-dimensional regular cubic lattices. 0000008222 00000 n Coordination number correlation function C(r) and its integral D(r) vs. distance r averaged over 10 7 lattices of 24 2 sites. The phase-transition location in the parameter space found by diffusion maps matched the theoretical position. Local properties and phase transitions in Sn doped antiferroelectric PbHfO 3 single crystal. 'Correlation Functions and their Generating Functionals: General Relations with Applications to the Theory of Fluids', by G. Stell. The system therefore undergoes a phase transition in which \(M\) changes discontinuously as it crosses over the coexistence curve at \(H=0\). rare region. A cumulant expansion is used to calculate the transition temperature of Ising models with random-bond defects. (3), corresponds to the one that characterizes the quenched RFIM. Although we do not have evidences that the double-gaussian distribution for the random fields can be realized experimentally, we can argue that this distribution is suitable for an appropriate theoretical description of random-field models [9]. We performed Monte Carlo simulations and our results suggest that first-order phase transitions occur in the model for some values of σ>0 at low temperatures and high random-field intensities. A central question is if the RR effects are strong enough to alter the phase transition, First-order phase transitions, classical or quantum, subject to randomness I will emphasize on thermodynamic versus geometric aspects of phase transitions both for the regular lattice and for the complete graph. recently established general relation between the Harris criterion and These results explain a host of puzzling violations of These are examples of phase transitions. such model, quantum three-color Ashkin-Teller model and show that the quantum B. N. Metropolis, A. W. Rosenbluth, N. M. Rosenbluth, A. H. Teller and E. Teller, J. Chem. 'Critical Point Statistical Mechanics and Quantum Field Theory', by G.A. These effects do not seem to be correctly described by annealed systems, where the change with time of the spatial distribution of Jij and/or hi is constrained by the need to reach equilibrium with the other degrees of freedom [10, 11, 12, 13, 14]. Following the success of the Ising model to capture the essential physics of complex systems, several lattice models have been proposed [8]. D. P. Belanger, A. R. King, V. Jaccarino, J. L. Cardy, Phys. The calculated runaway exponent yR of the renormalization-group flows decreases with increasing frustration to yR=0 when the spin-glass phase disappears. 'Computer Techniques for Evaluating Lattice Constants', by J.L. The critical behavior of this transition does not depend on the disorder strength, i.e., it is universal. This system differs from the standard equilibrium ones: while the local field is randomly assigned in space according to a distribution P(hi), which remains frozen in for the quenched case, and P(hi) contains essential correlations in the annealed system, where the impurity distribution is in equilibrium with the spin system, our case is similar to the quenched system at each time during the stationary regime, but hi keeps randomly changing with time, also according to P(hi), at each site i. and the random fields {hi} follow a continuous probability distribution, namely, the double-gaussian one. The diffusion-maps method is a kind of manifold learning algorithm, which tries to find a lower-dimensional representation of data. J. M. González-Miranda, A. Labarta, M. Puma, J. F. Fernández, P. L. Garrido and J. Marro, Phys. (4). The threshold value of σ, for which the phase transitions are always continuous, is difficult to determine numerically. Rev. However, first-order phase transitions may occur in the system for low temperatures and high random-field intensities ho, for some values of the parameter σ. All rights reserved. Its two triangular sublattices can be staggered in energy. That study showed a rich behavior of the system, with continuous and first-order phase transitions as well as a change in the concavity of the Almeida-Thouless (AT) line [30], which was experimentally verified in the diluted antiferromagnets FexZn1−xF2 [31]. They are characterized by a frozen-in spatial distribution of disorder, i.e., Jij and/or hi vary at random with i but remains fixed with time. Semantic Scholar is a free, AI-powered research tool for scientific literature, based at the Allen Institute for AI. In the past, scientists have tried using neural networks or unsupervised learning methods to identify phase transitions in experimental data, but these methods need trainable data or knowledge of the experimental set-up. 'Renormalization Group Theory of Interfaces', by D. Jasnow. The instantaneous Hamiltonian, Eq. Microscopic random quenched impurities may or may not produce rounding of a first-order phase transition. (2) is the Gibbs state corresponding to energy given by Eq. Their method can potentially help analyse data from complex quantum many-body experiments and improve our understanding of topological phases. C: Solid State Phys. (4); then, every lattice site is visited, and a spin flip occurs according to Metropolis’ rule. Corpus ID: 117993636. (2), the lattice is subdivided into spatial blocks of length and is the standard deviation of the block-averaged coordination numbers from the asymptotic mean value. Machine-learning tools also help researchers with the interpretation of the large amounts of data generated from modern experiments with many degrees of freedom.