We study the stochastic parallel dynamics of Ising spin systems defined on finitely connected directed random graphs with arbitrary degree distributions, using generating functional analysis. For fully asymmetric graphs the dynamics of the system can be completely solved, due to the asymptotic absence of loops. For arbitrary graph symmetry, we solve the dynamics exactly for the first few time steps, and we construct approximate stationary solutions.
We start from the Theory of Random Point Processes to derive n-point coupled master equations describing the continuous dynamics of discrete variables in random graphs. These equations constitute a hierarchical set of approximations that generalize and improve the Cavity Master Equation (CME) recently obtained in other publications. Our derivation clarifies some of the hypotheses and approximations that originally lead to the CME, considered now as the first order of a more general technique. We tested the new scheme in the dynamics of three models defined over diluted graphs: the Ising ferrom…
We prove that the variance of spin overlap vanishes in disordered Ising models satisfying the Fortuin-Kasteleyn-Ginibre (FKG) inequality under a uniform field, such as generally distributed random field Ising model, site- and bond-diluted Ising models with the Bernoulli distribution. Chatterjee's proof for the Gaussian random field Ising model is generalized to other independent identically distributed quenched disorder under a uniform field.
We study the dynamic and metastable properties of the fully connected Ising $p$-spin model with finite number of variables. We define trapping energies, trapping times and self correlation functions and we analyse their statistical properties in comparison to the predictions of trap models.
We consider the $\pm J$ Ising model on a cubic lattice with a gauge-invariant disorder distribution. Disorder depends on a parameter $β_G$ that plays the role of a chemical potential for the amount of frustration. We study the model at a specific value of the disorder parameter $β_G$, where frustration shows long-range correlations. We characterize the universality class, obtaining accurate estimates of the critical exponents: $ν= 0.655(15)$ and $η_q = 1.05(5)$, where $η_q$ is the overlap susceptibility exponent.
We apply support vector machine (SVM) to study the phase transition between many-body localized and thermal phases in a disordered quantum Ising chain in a transverse external field. The many-body eigenstate energy $E$ is bounded by a bandwidth $W=E_{max}-E_{min}$. The transition takes place on a phase diagram spanned by the energy density $ε=2(E-E_{min})/W$ and the disorder strength $δJ$ of the spin interaction uniformly distributed within $[-δJ, δJ]$, formally parallel to the mobility edge in Anderson localization. In our study we use the labeled probability density of eigenstate wavefunctio…
We study the low temperature out of equilibrium Monte Carlo dynamics of the disordered Ising $p$-spin Model with $p=3$ and a small number of spin variables. We focus on sequences of configurations that are stable against single spin flips obtained by instantaneous gradient descent from persistent ones. We analyze the statistics of energy gaps, energy barriers and trapping times on sub-sequences such that the overlap between consecutive configurations does not overcome a threshold. We compare our results to the predictions of various trap models finding the best agreement with the step model wh…
Spin Glass Transition at Nonzero Temperature in a Disordered Dipolar Ising System: The Case of LiHoxY{1-x}F4
自旋玻璃态是凝聚态物理中最有趣的问题之一，它的磁矩（自旋）冻结在随机方向上。虽然大多数理论研究都集中在爱德华-安德森模型的伊辛自旋只有离散的“上/下”方向，这样的伊辛系统是罕见的实验。LiHo $_{x}$ Y $_{1-x}$ F $_{4}$是一种几乎理想的Ising SG材料，其中Ho $^{3+}$矩由Ising自旋很好地描述。在LiHo $_{x}$ Y $_{1-x}$ F $_{4}$中，Ho $^{3+}$磁矩主要通过固有的受抑静磁偶极-偶极相互作用相互作用。导致SG行为的随机阻挫源自偶极耦合Ho $^{3+}$被非磁性Y $^{3+}$随机取代。在本文中，我们提供了令人信服的证据，从广泛的计算机模拟SG过渡在非零温度下发生在一个现实的微观模型LiHo $_{x}$ Y $_{1-x}$ F $_{4}$，从而解决了长期存在的，仍然在进行中，争议的SG过渡无序偶极伊辛系统的存在。
Motivated by the compound ${\rm LiHo}_x{\rm Y}_{1-x}{\rm F}_4$, we consider the Ising chain with random couplings and in the presence of simultaneous random transverse and longitudinal fields, and study its low-energy properties at zero temperature by the strong disorder renormalization group approach. In the absence of longitudinal fields, the system exhibits a quantum-ordered and a quantum-disordered phase separated by a critical point of infinite disorder. When the longitudinal random field is switched on, the ordered phase vanishes and the trajectories of the renormalization group are attr…
We study the out-of-equilibrium dynamics in the quantum Ising model with power-law interactions and positional disorder. For arbitrary dimension $d$ and interaction range $α\geq d$ we analytically find a stretched exponential decay of the global magnetization and ensemble-averaged single-spin purity with a stretch-power $β= d/α$ in the thermodynamic limit. Numerically, we confirm that glassy behavior persists for finite system sizes and sufficiently strong disorder. We identify dephasing between disordered coherent pairs as the main mechanism leading to a relaxation of global magnetization, wh…
Renyi Mutual information (RMI), computed from second Renyi entropies, can identify classical phase transitions from their finite-size scaling at the critical points. We apply this technique to examine the presence or absence of finite temperature phase transitions in various two-dimensional models on a square lattice, which are extensions of the conventional Ising model by adding a quenched disorder. When the quenched disorder causes the nearest neighbor bonds to be both ferromagnetic and antiferromagnetic, (a) a spin glass phase exists only at zero temperature, and (b) a ferromagnetic phase e…
Random transverse and longitudinal field Ising chains
Szeged University（塞格德大学）；HUN-REN Wigner Research Centre for Physics, Institute for Solid State Physics and Optics（匈牙利研究与教育网络维格纳物理研究中心固体物理与光学研究所）；Northwestern University（西北大学）
Stability of the symmetry-protected topological phase and Ising transitions in a disordered U(1) quantum link model on a ladder
Instytut Fizyki Teoretycznej, Uniwersytet Jagielloński（雅盖隆大学理论物理研究所）；Instituto de Fisica Fundamental IFF-CSIC（西班牙高等科学研究理事会基础物理研究所）；Institut de Ciencies Fotoniques (ICFO)（光子科学研究所）；Mark Kac Complex Systems Research Center, Uniwersytet Jagielloński（雅盖隆大学马克·卡克复杂系统研究中心）；Department of Physics, Indian Institute of Technology Madras（马德拉斯印度理工学院物理系）；Center for Quantum Information, Communication and Computation (CQuICC), Indian Institute of Technology Madras（马德拉斯印度理工学院量子信息、通信与计算中心）
We present a stochastic algorithm for constructing a topologically disordered (i.e., non-regular) spatial lattice with nodes of constant coordination number, the CC lattice. The construction procedure dramatically improves on an earlier proposal [Phys. Rev. E. 97, 022144 (2018)] with respect to both computational complexity and finite-size scaling properties - making the CC lattice an alternative to proximity graphs which, especially in higher dimensions, is significantly faster to build. Among other applications, physical systems such as certain amorphous materials with low concentration of c…
