Evidence against a mean field description of short-range spin glasses revealed through thermal boundary conditions

Abstract

A theoretical description of the low-temperature phase of short-range spin glasses has remained elusive for decades. In particular, it is unclear if theories that assert a single pair of pure states, or theories that are based infinitely many pure states-such as replica symmetry breaking-best describe realistic short-range systems. To resolve this controversy, the three-dimensional Edwards-Anderson Ising spin glass in thermal boundary conditions is studied numerically using population annealing Monte Carlo. In thermal boundary conditions all eight combinations of periodic vs antiperiodic boundary conditions in the three spatial directions appear in the ensemble with their respective Boltzmann weights, thus minimizing finite-size corrections due to domain walls. From the relative weighting of the eight boundary conditions for each disorder instance a sample stiffness is defined, and its typical value is shown to grow with system size according to a stiffness exponent. An extrapolation to the large-system-size limit is in agreement with a description that supports the droplet picture and other theories that assert a single pair of pure states. The results are, however, incompatible with the mean-field replica symmetry breaking picture, thus highlighting the need to go beyond mean-field descriptions to accurately describe short-range spin-glass systems.

13 pages, 11 figures, 3 tables

References in corpus (11)

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• Experimental Quantum Computations on a Topologically Encoded Qubit
• Error Threshold for Color Codes and Random 3-Body Ising Models
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Matching Kasteleyn Cities for Spin Glass Ground States
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• Correlations between the dynamics of parallel tempering and the free-energy landscape in spin glasses
• Scaling Analysis of Domain-Wall Free-Energy in the Edwards-Anderson Ising Spin Glass in a Magnetic Field
• Some considerations of finite dimensional spin glasses
• The cumulative overlap distribution function in realistic spin glasses

Cited by in corpus (9)

• Comparing Monte Carlo methods for finding ground states of Ising spin glasses: population annealing, simulated annealing and parallel tempering
• Number of thermodynamic states in the three-dimensional Edwards-Anderson spin glass
• Transitions From Order to Disorder in Multi-Dark and Multi-Dark-Bright Soliton Atomic Clouds
• Patch-planting spin-glass solution for benchmarking
• Non-equilibrium evolution of window overlaps in spin glasses
• Critical Point Scaling of Ising Spin Glasses in a Magnetic Field
• Ground state interface exponents of the diluted Sherrington-Kirkpatrick spin glass
• Measuring free energy in parallel tempering Monte Carlo
• Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman