One-dimensional infinite component vector spin glass with long-range interactions

Abstract

We investigate zero and finite temperature properties of the one-dimensional spin-glass model for vector spins in the limit of an infinite number m of spin components where the interactions decay with a power, σ, of the distance. A diluted version of this model is also studied, but found to deviate significantly from the fully connected model. At zero temperature, defect energies are determined from the difference in ground-state energies between systems with periodic and antiperiodic boundary conditions to determine the dependence of the defect-energy exponent θon σ. A good fit to this dependence is θ=3/4-σ. This implies that the upper critical value of σis 3/4, corresponding to the lower critical dimension in the d-dimensional short-range version of the model. For finite temperatures the large m saddle-point equations are solved self-consistently which gives access to the correlation function, the order parameter and the spin-glass susceptibility. Special attention is paid to the different forms of finite-size scaling effects below and above the lower critical value, σ=5/8, which corresponds to the upper critical dimension 8 of the hypercubic short-range model.

27 pages, 27 figures, 4 tables

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• Finite-size scaling above the upper critical dimension in Ising models with long-range interactions
• Domain-wall excitations in the two-dimensional Ising spin glass
• Approximating the XY model on a random graph with a $q$-state clock model
• Clock Monte Carlo methods
• The 1/m expansion in spin glasses and the de Almeida-Thouless line
• Cluster Monte Carlo and dynamical scaling for long-range interactions
• Random Coulomb antiferromagnets: from diluted spin liquids to Euclidean random matrices
• Ordering Dynamics of the Random Field Long-range Ising Model in One Dimension
• Infinite randomness critical behavior of the contact process on networks with long-range connections
• Study of the de Almeida-Thouless (AT) line in the one-dimensional diluted power-law XY spin glass
• Infinite volume extrapolation in the one-dimensional bond diluted Levy spin-glass model near its lower critical dimension
• Inherent Structures in m-component Spin Glasses
• Mean-field theory is exact for Ising spin glass models with Kac potential in non-additive limit on Nishimori line
• Critical properties of disordered XY model on sparse random graphs
• Domain Growth in Long-range Ising Models with Disorder