Interface free-energy exponent in the one-dimensional Ising spin glass with long-range interactions in both the droplet and broken replica symmetry regions

Abstract

The one-dimensional Ising spin-glass model with power-law long-range interactions is a useful proxy model for studying spin glasses in higher space dimensions and for finding the dimension at which the spin-glass state changes from having broken replica symmetry to that of droplet behavior. To this end we have calculated the exponent that describes the difference in free energy between periodic and antiperiodic boundary conditions. Numerical work is done to support some of the assumptions made in the calculations and to determine the behavior of the interface free-energy exponent of the power law of the interactions. Our numerical results for the interface free-energy exponent are badly affected by finite-size problems.

10 pages, 5 figures, 3 tables

References in corpus (12)

• Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses
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Cited by in corpus (13)

• Number of thermodynamic states in the three-dimensional Edwards-Anderson spin glass
• The Fractal Dimension of Interfaces in Edwards-Anderson and Long-range Ising Spin Glasses: Determining the Applicability of Different Theoretical Descriptions
• The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
• Chaotic temperature and bond dependence of four-dimensional Gaussian spin glasses with partial thermal boundary conditions
• Ground State Properties of the Diluted Sherrington-Kirkpatrick Spin Glass
• Study of the de Almeida-Thouless (AT) line in the one-dimensional diluted power-law XY spin glass
• Evidence that the AT transition disappears below six dimensions
• Evidence of many thermodynamic states of the three-dimensional Ising spin glass
• Numerical simulations of Ising spin glasses with free boundary conditions: the role of droplet excitations and domain walls
• Cycle-expansion method for the Lyapunov exponent, susceptibility, and higher moments
• Triviality of the ground-state metastate in long-range Ising spin glasses in one dimension
• Nature of spin glass order in physical dimensions
• Ground state interface exponents of the diluted Sherrington-Kirkpatrick spin glass