We show that the Almeida-Thouless line in Ising spin glasses vanishes when their dimension d -> 6 as h_{AT}^2/T_c^2 = C(d-6)^4(1- T/T_c)^{d/2 - 1}, where C is a constant of order unity. An equivalent result which could be checked by simulations is given for the one-dimensional Ising spin glass with long-range interactions. It is shown that replica symmetry breaking also stops as d -> 6.
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…
We study the phase transition of the free energy in the Sherrington-Kirkpatrick mean-field spin glass model with centered Gaussian external field. We show that the corresponding Almeida-Thouless line is the correct transition curve that distinguishes between the replica symmetric and replica symmetry breaking solutions in the Parisi formula.
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…
We determine explicitly and discuss in detail the effects of the joint presence of a longitudinal and a transversal (random) magnetic field on the phases of the Random Energy Model (REM) and its hierarchical generalization, the GREM. Our results extent known results both in the classical case of vanishing transversal field and in the quantum case for vanishing longitudinal field. Following Derrida and Gardner, we argue that the longitudinal field has to be implemented hierarchically also in the Quantum GREM. We show that this ensures the shrinking of the spin glass phase in the presence of the…
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…
Aging dynamics across a dynamic Almeida-Thouless line in three dimensional short-range Issuing spin glass Cu$_{0.5}$Co$_{0.5}$Cl$_{2}$-FeCl$_{3}$ graphite bi-intercalation compound
Cu $_{0.5}$ Co $_{0.5}$ Cl $_{2}$ -FeCl $_{3}$石墨层间化合物是具有自旋冻结温度$T_{c}$（$= 3.92 \pm 0.11$ K）的三维短程伊辛自旋玻璃。在磁场$H$存在下的自旋玻璃相的稳定性由（i）自旋冻结温度$T_{f}(ω,H)$检验，在该温度下，微分场冷却（FC）磁化率$\partial M_{FC}(T,H)/\partial H$与具有角频率$ω$的色散$χ^{\prime}(ω,T,H=0)$一致，以及（ii）在具有等待时间$t_{W}$（$= 1.0 \times 10^{4}$）的ZFC老化协议之后，零场冷却（ZFC）磁化率$χ_{ZFC}$的时间依赖性。弛豫速率$S(t)$（= d $χ_{ZFC}$ /d $\ln t$）在特征时间$t_{cr}$处表现出局部最大值，反映了非平衡老化动力学。在固定温度$T$（2.9 K $\leq T<T_{c}$）下，峰值时间$t_{cr}(T,H)$随$H$的增加而减小。自旋冻结温度$T_{f}(ω,H)$提供了在有限磁场中热平衡时自旋玻璃相不稳定的证据。$t_{cr}(T,H)$和$T_{f}(ω,H)$都表现出一定的缩放行为预测的液滴图片，表明在$H$的存在下，从SG动态顺磁行为的动态交叉。
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。
Spin glasses in a field: Three and four dimensions as seen from one space dimension
我们研究了在磁场中的伊辛自旋玻璃的跃迁线的存在性-被称为德阿尔梅达无磁线-使用一维幂律稀释伊辛自旋玻璃模型。我们选择幂律指数具有近似对应于三维和四维最近邻系统的值，并对大型线性系统尺寸的数据进行详细的有限尺寸标度分析，两者都使用最近提出的新方法[Phys. Rev. Lett. 103，267201（2009）]以及传统方法。虽然新的有限尺寸标度方法并不排除一种可能性，但我们对三维系统模型的研究结果与没有德阿尔梅达无边界线的结论是一致的。对于对应于四个空间维度的模型，新的和传统的有限尺寸标度分析给出了相互矛盾的结果，表明需要更好地理解自旋玻璃在磁场中的有限尺寸标度。
We propose an iterative algorithm for solving the Thouless-Anderson-Palmer (TAP) equations of Ising models with arbitrary rotation invariant (random) coupling matrices. In the thermodynamic limit, we prove by means of the dynamical functional method that the proposed algorithm converges when the so-called de Almeida Thouless (AT) criterion is fulfilled. Moreover, we give exact analytical expressions for the rate of the convergence.
We discuss a phase transition in spin glass models which have been rarely considered in the past, namely the phase transition that may take place when two real replicas are forced to be at a larger distance (i.e. at a smaller overlap) than the typical one. In the first part of the work, by solving analytically the Sherrington-Kirkpatrick model in a field close to its critical point, we show that even in a paramagnetic phase the forcing of two real replicas to an overlap small enough leads the model to a phase transition where the symmetry between replicas is spontaneously broken. More importan…
