Diluted one-dimensional spin glasses with power law decaying interactions

Abstract

We introduce a diluted version of the one dimensional spin-glass model with interactions decaying in probability as an inverse power of the distance. In this model varying the power corresponds to change the dimension in short-range models. The spin-glass phase is studied in and out of the range of validity of the mean-field approximation in order to discriminate between different theories. Since each variable interacts only with a finite number of others the cost for simulating the model is drastically reduced with respect to the fully connected version and larger sizes can be studied. We find both static and dynamic evidence in favor of the so-called replica symmetry breaking theory.

4 pages, 6 figures, 2 tables

References in corpus (15)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• The Bethe lattice spin glass revisited
• Critical exponents of the three dimensional diluted Ising model
• Geometrical Aspects of Aging and Rejuvenation in the Ising Spin Glass: A Numerical Study
• Off-Equilibrium Dynamics in Finite-Dimensional Spin Glass Models
• Spin and link overlaps in 3-dimensional spin glasses
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Criticality in one dimension with inverse square-law potentials
• Off-Equilibrium Dynamics at Very Low Temperatures in 3d Spin Glasses
• Ultrametricity in the Edwards-Anderson Model
• Geometry of large-scale low-energy excitations in the one-dimensional Ising spin glass with power-law interactions
• Critical behaviour and ultrametricity of Ising spin-glass with long-range interactions
• Scaling and infrared divergences in the replica field theory of the Ising spin glass
• Local Spin Glass Order in 1D
• Non-trivial link overlap distribution in three-dimensional Ising spin glasses

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• Numerical studies of a one-dimensional 3-spin spin-glass model with long-range interactions
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• Imry-Ma criterion for long-range random field Ising model: short-/long-range equivalence in a field
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• One-dimensional infinite component vector spin glass with long-range interactions
• Finite-size critical scaling in Ising spin glasses in the mean-field regime
• The ordered phase of the one-dimensional Ising spin glass with long-range interactions
• The Ising M-p-spin mean-field model for the structural glass: continuous vs. discontinuous transition
• Phase Transitions in the 1-d Long-Range Diluted Heisenberg Spin Glass
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• Study of the de Almeida-Thouless line using one-dimensional power-law diluted Heisenberg Spin Glasses
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• The low-temperature phase in the two-dimensional long-range diluted XY model
• Spin-chirality decoupling in the one-dimensional Heisenberg spin glass with long-range power-law interactions
• Scaling of the largest dynamical barrier in the one-dimensional long-range Ising spin-glass
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