De Almeida-Thouless Transition Research Articles

Gardner Transition in Physical Dimensions.

The Gardner transition is the transition that at mean-field level separates a stable glass phase from a marginally stable phase. This transition has similarities with the de Almeida-Thouless transition of spin glasses. We have studied a well-understood problem, that of disks moving in a narrow channel, which shows many features usually associated with the Gardner transition. We show that some of these features are artifacts that arise when a disk escapes its local cage during the quench to higher densities. There is evidence that the Gardner transition becomes an avoided transition, in that the correlation length becomes quite large, of order 15 particle diameters, even in our quasi-one-dimensional system.

Nontrivial Critical Fixed Point for Replica-Symmetry-Breaking Transitions.

The transformation of the free-energy landscape from smooth to hierarchical is one of the richest features of mean-field disordered systems. A well-studied example is the de Almeida-Thouless transition for spin glasses in a magnetic field, and a similar phenomenon-the Gardner transition-has recently been predicted for structural glasses. The existence of these replica-symmetry-breaking phase transitions has, however, long been questioned below their upper critical dimension, d_{u}=6. Here, we obtain evidence for the existence of these transitions in d<d_{u} using a two-loop calculation. Because the critical fixed point is found in the strong-coupling regime, we corroborate the result by resumming the perturbative series with inputs from a three-loop calculation and an analysis of its large-order behavior. Our study offers a resolution of the long-lasting controversy surrounding phase transitions in finite-dimensional disordered systems.

Finite-size critical scaling in Ising spin glasses in the mean-field regime.

We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one-dimensional spin-glass models with power-law long-range interactions in the regime where they can be a proxy for the Edwards-Anderson short-range spin-glass model above the upper critical dimension. We also calculate a simple analytical approximation for the spin-glass susceptibility crossover function. The behavior of the spin-glass susceptibility near the de Almeida-Thouless transition line has also been studied, but here we have only been able to obtain analytically its behavior in the asymptotic limit above and below the transition. We have also simulated the one-dimensional system in a field in the non-mean-field regime to illustrate that when the Imry-Ma droplet length scale exceeds the system size one can then be erroneously lead to conclude that there is a de Almeida-Thouless transition even though it is absent.

Evolution from a ferromagnetic to a spin-glass regime in the spinel-type [formula omitted

Successive changes from ferromagnetic, re-entrant mixed, to spin-glass regime have been manifestly found with increasing Ti-composition x in the quaternary spinel-type Cu ( Cr 1 - x Ti x ) 2 S 4 system. The Curie temperature T c decreases steeply with increasing x and this transition becomes ill-defined around x = 0.47 . Two distinct transitions appear below T c over the range x = 0.40 – 0.47 . Coexistence of the ferromagnetism and spin-glass order would be observed below the Gabay and Toulouse transition ( T GT ), owing to freezing of the transverse-spin components without changing of the ferromagnetic order parameter. Finally, at a yet lower temperature de Almeida–Thouless transition ( T AT ), the longitudinal-spin component freezes randomly at which an irreversibility arises between zero-field-cooled (ZFC) and field-cooled (FC) magnetizations. Over the range of 0.47 ⩽ x ⩽ 0.85 , a cusp of the ZFC magnetization is seen at T g like conventional spin-glass. Specimens with x ⩾ 0.90 remain paramagnetic down to 2.0 K. A magnetic phase diagram between T versus x has been obtained experimentally. The values of the multicritical point in 100 Oe is detected to be x = 0.47 and T = 7.40 K . The low-field magnetization and the phase diagram are satisfactorily explained by the theory of Gabay and Toulouse on the basis of Heisenberg isotropic vector spin model rather than the Ising spin model.

Near-optimal configurations in mean-field disordered systems.

We present a general technique to compute how the energy of a configuration varies as a function of its overlap with the ground state in the case of optimization problems. Our approach is based on a generalization of the cavity method to a system interacting with its ground state. With this technique we study the random matching problem as well as the mean-field diluted spin glass. As a by-product of this approach we calculate the de Almeida-Thouless transition line of the spin glass on a fixed connectivity random graph.

Generic replica symmetric field-theory for short range Ising spin glasses

Symmetry considerations and a direct, Hubbard-Stratonovich type, derivation are used to construct a replica field-theory relevant to the study of the spin glass transition of short range models in a magnetic field. A mean-field treatment reveals that two different types of transitions exist, whenever the replica number n is kept larger than zero. The Sherrington-Kirkpatrick critical point in zero magnetic field between the paramagnet and replica magnet (a replica symmetric phase with a nonzero spin glass order parameter) separates from the de Almeida-Thouless line, along which replica symmetry breaking occurs. We argue that for studying the de Almeida-Thouless transition around the upper critical dimension d=6, it is necessary to use the generic cubic model with all the three bare masses and eight cubic couplings. The critical role n may play is also emphasized. To make perturbative calculations feasible, a new representation of the cubic interaction is introduced. To illustrate the method, we compute the masses in one-loop order. Some technical details and a list of vertex rules are presented to help future renormalisation-group calculations.

The irreversibility line and a free energy expansion

The mixed state of extreme type II superconductors display two distinguishable regions, associated with a resistive and a true superconducting state. In the vicinity of T c , I take that the description of these two regions, for the low temperature isotropic superconductors, is possible in terms of a free energy expansion. For large κ materials 1 find that de Almeida-Thouless transition and the coexistence of normal and superconducting phases are natural consequences of the free energy expansion proposed here.

Spin-glass freezing and universal scaling in Cd 1−xMn xTe

Static low-field longitudinal magnetic susceptibility χ( T), of Cd 1- x Mn x Te ( x = 0.3, 0.4, 0.45 and 0.55) was determined by SQUID susceptibility. All archetypal spin-glass (SG) ordering behaviors were observed. From a Fischer-type model of the low-temperature susceptibility χ( T), we have determined the Edwards-Anderson (EA) spin-glass order parameter, q( T). Unlike static magnetization and specific heat results where classical scaling predictions are known to fail for this system, q( T) shows excellent agreement with mean field Ising-type model scaling predictions. It is argued that the criticality is related to a de Almeida-Thouless transition.

Ordered phase of short-range Ising spin-glasses.

We propose a new picture of the Ising-spin-glass phase, based on an Ansatz for the scaling of low-lying large-scale-droplet excitations. We find behavior very different from the infinite-range model. The truncated spatial correlations decay as a power of distance, the ac nonlinear susceptibility diverges as a power of $\mathrm{ln}\ensuremath{\omega}$, and the magnetization noise power diverges as $\frac{1}{\ensuremath{\omega}}$ with logarithmic corrections. A magnetic field destroys the spin-glass phase so that there is no de Almeida-Thouless transition. Defect excitations should yield similar dynamic phenomena in vector spin-glasses.

Experimental search for the spin-glass transition in Eu 0.4Sr 0.6S: A dynamic scaling analysis

We first present a scaling argument for the relaxation times in spin glasses, as suggested by Binder and Young. We emphasize the relevance of our dynamic measurements near the magnetic field-temperature transition line to equilibrium properties such as the nonlinear susceptibility. We show how, in the insulating system Eu 0.4Sr 0.6S, the phase lag of the ac susceptibility with respect to the modulated field relates the measuring frequency ω to a characteristic response time τ. We are thus able to define the zero field freezing temperature, T f(ω). Two scaling models are tested, appropriate to a finite critical temperature, T c, and to a zero temperature transition. Respectively, this leads to two critical slowing down regimes: τ/τ 0 ∼ ( T - T c) -zv and ln(τ/τ 0) ∼ T -zv. Both are shown to be consistent with the data, and to lead to T c = 1.50 K, zv = 8, τ 0 = 3x10 -12 s; or T c = 0, zv = 9 and τ 0 = 10 -8 s. The set of parameters derived for the former (finite T c) case appears to be more consistent with previous data on Eu 0.4Sr 0.6S, and with recent computer simulations. We then generate, in the magnetic field-temperature plane, lines T f (ω, H) associated with the response time τ. We include remanent magnetization measurements which refer to well defined experimental time scales (⩽1 s or ⩽25 s). The entire set of scaled data, for the case when T c = 1.50 K, strongly suggests that the response time diverges for H 1 2 ∼ T − T c . This is of the form of a de Almeida-Thouless transition line with, however, a non-mean-field exponent.

Threshold field for the de Almeida–Thouless transition line in Eu0.4Sr0.6S spin glass

Measurements of the imaginary component of the ac magnetic susceptibility of a spherical sample of Eu0.4Sr0.6S at frequencies between 7 Hz and 5 kHz reveal that the temperature for the onset of hysteresis decreases as approximately Ha2/3 in an applied dc magnetic field Ha but only when the field exceeds a frequency-dependent threshold H0( f). This threshold also marks the onset for nonlinearity in the real component of the susceptibility and thus delineates two regions of distinctly different dynamical response.