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Almeida-Thouless transition below six dimensions  [PDF]
Tamás Temesvári
Physics , 2008, DOI: 10.1103/PhysRevB.78.220401
Abstract: The existence of an Almeida-Thouless (AT) instability surface below the upper critical dimension 6 is demonstrated in the generic replica symmetric field theory. Renormalization flows from around the zero-field fixed point are investigated. By introducing the temperature and magnetic field dependence of the bare parameters, the fate of the AT line can be followed from mean field (infinite dimensions) down to d<6.
Absence of an Almeida-Thouless line in Three-Dimensional Spin Glasses  [PDF]
A. P. Young,Helmut G. Katzgraber
Physics , 2004, DOI: 10.1103/PhysRevLett.93.207203
Abstract: We present results of Monte Carlo simulations of the three-dimensional Edwards-Anderson Ising spin glass in the presence of a (random) field. A finite-size scaling analysis of the correlation length shows no indication of a transition, in contrast to the zero-field case. This suggests that there is no Almeida-Thouless line for short-range Ising spin glasses.
Probing the Almeida-Thouless line away from the mean-field model  [PDF]
Helmut G. Katzgraber,A. P. Young
Physics , 2005, DOI: 10.1103/PhysRevB.72.184416
Abstract: Results of Monte Carlo simulations of the one-dimensional long-range Ising spin glass with power-law interactions in the presence of a (random) field are presented. By tuning the exponent of the power-law interactions, we are able to scan the full range of possible behaviors from the infinite-range (Sherrington-Kirkpatrick) model to the short-range model. A finite-size scaling analysis of the correlation length indicates that the Almeida-Thouless line does not occur in the region with non-mean-field critical behavior in zero field. However, there is evidence that an Almeida-Thouless line does occur in the mean-field region.
The de Almeida-Thouless line in vector spin glasses  [PDF]
Auditya Sharma,A. P. Young
Physics , 2010, DOI: 10.1103/PhysRevE.81.061115
Abstract: We consider the infinite-range spin glass in which the spins have m > 1 components (a vector spin glass). Applying a magnetic field which is random in direction, there is an Almeida Thouless (AT) line below which the "replica symmetric" solution is unstable, just as for the Ising (m=1) case. We calculate the location of this AT line for Gaussian random fields for arbitrary m, and verify our results by numerical simulations for m = 3$.
Disappearance of the de Almeida-Thouless line in six dimensions  [PDF]
M. A. Moore,A. J. Bray
Physics , 2011, DOI: 10.1103/PhysRevB.83.224408
Abstract: 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.
The 1/m expansion in spin glasses and the de Almeida-Thouless line  [PDF]
M. A. Moore
Physics , 2012, DOI: 10.1103/PhysRevE.86.031114
Abstract: It is shown by means of a 1/m expansion about the large-m limit of the m-vector spin glass that the lower critical dimension of the de Almeida-Thouless line in spin glasses is equal to the lower critical dimension of the large-m limit of the m-vector spin glass. Numerical studies suggest that this is close to six.
Evidence against an Almeida-Thouless line in disordered systems of Ising dipoles  [PDF]
Julio F. Fernandez
Physics , 2010, DOI: 10.1103/PhysRevB.82.144436
Abstract: By tempered Monte Carlo simulations, an Almeida-Thouless (AT) phase-boundary line in site-diluted Ising spin systems is searched for. Spins interact only through dipolar fields and occupy a small fraction of lattice sites. The spin-glass susceptibility of these systems and of the Sherrington-Kirkpatrick model are compared. The correlation length as a function of system size and temperature is also studied. The results obtained are contrary to the existence of an AT line.
Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses  [PDF]
Helmut G. Katzgraber,Derek Larson,A. P. Young
Physics , 2008, DOI: 10.1103/PhysRevLett.102.177205
Abstract: We test for the existence of a spin-glass phase transition, the de Almeida-Thouless line, in an externally-applied (random) magnetic field by performing Monte Carlo simulations on a power-law diluted one-dimensional Ising spin glass for very large system sizes. We find that an Almeida-Thouless line only occurs in the mean field regime, which corresponds, for a short-range spin glass, to dimension d larger than 6.
About the Almeida-Thouless transition line in the Sherrington-Kirkpatrick mean field spin glass mode  [PDF]
Fabio L. Toninelli
Physics , 2002, DOI: 10.1209/epl/i2002-00667-5
Abstract: We consider the Sherrington-Kirkpatrick model and we prove that the thermodynamic limit of the quenched free energy per site is strictly greater than the corresponding replica symmetric approximation, for all values of the temperature and of the magnetic field below the Almeida-Thouless line. This is based on recent rigorous bounds by F. Guerra, relating the true free energy of the system to the Parisi solution with replica symmetry breaking.
The replica symmetric region in the Sherrington-Kirkpatrick mean field spin glass model. The Almeida-Thouless line  [PDF]
Francesco Guerra
Physics , 2006,
Abstract: In previous work, we have developed a simple method to study the behavior of the Sherrington-Kirkpatrick mean field spin glass model for high temperatures, or equivalently for high external fields. The basic idea was to couple two different replicas with a quadratic term, trying to push out the two replica overlap from its replica symmetric value. In the case of zero external field, our results reproduced the well known validity of the annealed approximation, up to the known critical value for the temperature. In the case of nontrivial external field, our method could prove the validity of the Sherrington-Kirkpatrick replica symmetric solution up to a line, which fell short of the Almeida-Thouless line, associated to the onset of the spontaneous replica symmetry breaking, in the Parisi Ansatz. Here, we make a strategic improvement of the method, by modifying the flow equations, with respect to the parameters of the model. We exploit also previous results on the overlap fluctuations in the replica symmetric region. As a result, we give a simple proof that replica symmetry holds up to the critical Almeida-Thouless line, as expected on physical grounds. Our results are compared with the characterization of the replica symmetry breaking line previously given by Talagrand. We outline also a possible extension of our methods to the broken replica symmetry region.
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