Study of the de Almeida-Thouless (AT) line in the one-dimensional diluted power-law XY spin glass

Abstract

We study the AT line in the one-dimensional power-law diluted XY spin glass model, in which the probability that two spins separated by a distance $r$ interact with each other, decays as $1/r^{2\sigma }$. We develop a heat bath algorithm to equilibrate XY spins; using this in conjunction with the standard parallel tempering and overrelaxation sweeps, we carry out large scale Monte Carlo simulations. For $\sigma =0.6$ which is in the mean-field regime, we find clear evidence for an AT line. For $\sigma =0.75$, there is evidence from finite size scaling studies for an AT transition but for $\sigma =0.85$, the evidence for a transition is non-existent. We have also studied these systems at fixed temperature varying the field and discovered that at both $\sigma =0.75$ and at $\sigma =0.85$ there is evidence of an AT transition! Confusingly, the correlation length and spin glass susceptibility as a function of the field are both entirely consistent with the predictions of the droplet picture and hence the non-existence of an AT line. The evidence from our simulations points to the complete absence of the AT line in dimensions outside the mean-field region and to the correctness of the droplet picture. Previous simulations which suggested there was an AT line can be attributed to the consequences of studying systems which are just too small. The collapse of our data to the droplet scaling form is poor for $\sigma =0.75$ and to some extent also for $\sigma =0.85$, when the correlation length becomes of the order of the length of the system, due to the existence of excitations which only cost a free energy of $O(1)$, just as envisaged in the TNT picture of the ordered state of spin glasses. However, for the case of $\sigma =0.85$ we can provide evidence that for larger system sizes, droplet scaling will prevail even when the correlation length is comparable to the system size.

arXiv comment24 pages, 15 figures

References in corpus (39)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Nature of the Spin Glass State
• Monte Carlo Simulations of Spin Glasses at Low Temperatures
• Spin and link overlaps in 3-dimensional spin glasses
• Finite size effects on measures of critical exponents in d=3 O(N) models
• The critical behavior of three-dimensional Ising spin glass models
• Absence of an Almeida-Thouless line in Three-Dimensional Spin Glasses
• Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses
• Diluted one-dimensional spin glasses with power law decaying interactions
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Probing the Almeida-Thouless line away from the mean-field model
• Chiral-glass transition and replica symmetry breaking of a three-dimensional Heisenberg spin glass
• Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis
• Disappearance of the de Almeida-Thouless line in six dimensions
• Ising spin glass transition in magnetic field out of mean-field
• The spin glass transition of the three dimensional Heisenberg spin glass
• Large-scale Monte Carlo simulations of the isotropic three-dimensional Heisenberg spin glass
• Soft Modes, Localization and Two-Level Systems in Spin Glasses
• Numerical evidence of the spin-chirality decoupling in the three-dimensional Heisenberg spin glass
• The three dimensional Ising spin glass in an external magnetic field: the role of the silent majority
• The correspondence between long-range and short-range spin glasses
• A Monte Carlo study of O(3) antiferromagnetic models in three dimensions
• Strengths and Weaknesses of Parallel Tempering
• Numerical studies of a one-dimensional 3-spin spin-glass model with long-range interactions
• Large-scale Monte Carlo simulations of the three-dimensional XY spin glass
• The de Almeida-Thouless line in vector spin glasses
• Finite-size critical scaling in Ising spin glasses in the mean-field regime
• One-dimensional infinite component vector spin glass with long-range interactions
• The random field XY model on sparse random graphs shows replica symmetry breaking and marginally stable ferromagnetism
• Phase Transitions in the 1-d Long-Range Diluted Heisenberg Spin Glass
• The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
• Study of the de Almeida-Thouless line using one-dimensional power-law diluted Heisenberg Spin Glasses
• Interface free-energy exponent in the one-dimensional Ising spin glass with long-range interactions in both the droplet and broken replica symmetry regions
• The 1/m expansion in spin glasses and the de Almeida-Thouless line
• Finite-Dimensional Spin Glasses: States, Excitations, and Interfaces
• Delocalization transition in low energy excitation modes of vector spin glasses
• The metastable minima of the Heisenberg spin glass in a random magnetic field
• Comparison of Gabay-Toulouse and de Almeida-Thouless instabilities for the spin glass XY model in a field on sparse random graphs
• Avalanches and hysteresis in frustrated superconductors and XY-spin-glasses

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• Replica Symmetry Broken States of some Glass Models
• Canonical equilibrium of mean-field $O(n)$~models in the presence of random fields
• Evidence of de Almeida-Thouless line below six dimensions
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