We study, in random sparse networks, finite size scaling of the spin glass susceptibility $χ_{\rm SG}$, which is a proper measure of the de Almeida-Thouless (AT) instability of spin glass systems. Using a phenomenological argument regarding the band edge behavior of the Hessian eigenvalue distribution, we discuss how $χ_{\rm SG}$ is evaluated in infinitely large random sparse networks, which are usually identified with Bethe trees, and how it should be corrected in finite systems. In the high temperature region, data of extensive numerical experiments are generally in good agreement with the theoretical values of $χ_{\rm SG}$ determined from the Bethe tree. In the absence of external fields, the data also show a scaling relation $χ_{\rm SG}=N^{1/3}F(N^{1/3}|T-T_c|/T_c)$, which has been conjectured in the literature, where $T_c$ is the critical temperature. In the presence of external fields, on the other hand, the numerical data are not consistent with this scaling relation. A numerical analysis of Hessian eigenvalues implies that strong finite size corrections of the lower band edge of the eigenvalue distribution, which seem relevant only in the presence of the fields, are a major source of inconsistency. This may be related to the known difficulty in using only numerical methods to detect the AT instability.
This work contains a review of the theoretical understanding for the Almeida-Thouless transition. The effective field theoretic model for this transition to the replica symmetry broken phase is extended to low temperatures, making it possible to compute perturbative corrections to the mean field phase boundary even close to zero temperature. Nonperturbative behavior emerges both around the zero-external-field transition and at low temperature. Renormalization group results are also discussed.
Vector spin glasses are known to show two different kinds of phase transitions in presence of an external field: the so-called de Almeida-Thouless and Gabay-Toulouse lines. While the former has been studied to some extent on several topologies (fully connected, random graphs, finite-dimensional lattices, chains with long-range interactions), the latter has been studied only in fully connected models, which however are known to show some unphysical behaviors (e.g. the divergence of these critical lines in the zero-temperature limit). Here we compute analytically both these critical lines for XY…
The de Almeida-Thouless (AT) line in Ising spin glasses is the phase boundary in the temperature $T$ and magnetic field $h$ plane below which replica symmetry is broken. Using perturbative renormalization group (RG) methods, we show that when the dimension $d$ of space is just above $6$ there is a multicritical point (MCP) on the AT line, which separates a low-field regime, in which the critical exponents have mean-field values, from a high-field regime where the RG flows run away to infinite coupling strength; as $d$ approaches $6$ from above, the location of the MCP approaches the zero-field…
A replica-symmetry-breaking phase transition is predicted in a host of disordered media. The criticality of the transition has, however, long been questioned below its upper critical dimension, six, due to the absence of a critical fixed point in the renormalization-group flows at one-loop order. A recent two-loop analysis revealed a possible strong-coupling fixed point but, given the uncontrolled nature of perturbative analysis in the strong-coupling regime, debate persists. Here we examine the nature of the transition as a function of spatial dimension and show that the strong-coupling fixed…
The de Almeida-Thouless (AT) line is the phase boundary in the temperature--magnetic field plane of an Ising spin glass at which a continuous (i.e. second-order) transition from a paramagnet to a replica-symmetry-breaking (RSB) phase occurs, according to mean-field theory. Here, using field-theoretic perturbative renormalization group methods on the Bray-Roberts reduced Landau-Ginzburg-type theory for a short-range Ising spin glass in space of dimension $d$, we show that at nonzero magnetic field the nature of the corresponding transition is modified as follows: a) for $d-6$ small and positive…
Evidence of the de Almeida-Thouless transition in three-dimensional spin glasses
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Wenzhou Institute, University of Chinese Academy of Sciences（中国科学院大学温州研究院）
Comment on "Critical point scaling of Ising spin glasses in a magnetic field" by J. Yeo and M.A. Moore
在最近出版物的一部分中，[J. Yeo和M.A. Moore，Phys. Rev. B 91，104432（2015）]，作者讨论了Parisi和Temesvári [Nuclear Physics B 858，293（2012）]论文中的一些论点。在这篇评论中，它显示了这些论点是如何被误解的，并重申了在上临界维6中存在Almeida-Almeidless转变。
Use of dedicated computers in spin glass simulations allows one to equilibrate very large samples (of size as large as $L=32$) and to carry out "computer experiments" that can be compared to (and analyzed in combination with) laboratory experiments on spin-glass samples. In the absence of a magnetic field, the most economic conclusion of the combined analysis of equilibrium and non-equilibrium simulations is that an RSB spin glass phase is present in three spatial dimensions. However, in the presence of a field, the lower critical dimension for the de Almeida-Thouless transition seems to be la…
The Sherrington-Kirkpatrick spin glass model in the presence of a random field with a joint Gaussian probability density function for the exchange interactions and random fields
Instability of Laughlin FQH liquids into gapless power-law correlated states with continuous exponents in ideal Chern bands: rigorous results from plasma mapping
Institut für Theoretische Physik, Universität Leipzig（莱比锡大学理论物理研究所）
