Determining Energy Barriers by Iterated Optimization: The Two-Dimensional Ising Spin Glass

Abstract

Energy barriers determine the dynamics in many physical systems like structural glasses, disordered spin systems or proteins. Here we present an approach, which is based on subdividing the configuration space in a hierarchical manner, leading to upper and lower bounds for the energy barrier separating two configurations. The fundamental operation is to perform a constrained energy optimization, where the degree of constraintness increases with the level in the hierarchy. As application, we consider Ising spin glasses, where the energy barrier which needs to be surmounted in order to flip a compact region of spins of linear dimension $L$ are expected to scale as $L^{\psi }$. The exponent $\psi$ is very hard to estimate from experimental and simulation studies. By using the new approach, applying efficient combinatorial matching algorithms, we are able to give the first non-trivial numerical bounds $0.25<\psi <0.54$ for the two-dimensional Ising spin glass.

4 pages, 6 figures

References in corpus (9)

• Geometrical Aspects of Aging and Rejuvenation in the Ising Spin Glass: A Numerical Study
• The critical exponents of the two-dimensional Ising spin glass revisited: Exact Ground State Calculations and Monte Carlo Simulations
• Energetics and geometry of excitations in random systems
• Trivial Ground State Structure in the Two-Dimensional Ising Spin Glass
• Energy Barriers to Motion of Flux Lines in Random Media
• Corrections to Scaling are Large for Droplets in Two-Dimensional Spin Glasses
• Computational Complexity of Determining the Barriers to Interface Motion in Random Systems
• Energy Barriers for Flux Lines in 3 Dimensions
• Energy barriers in spin glasses

Cited by in corpus (6)

• Dynamical scaling in Ising and vector spin glasses
• The energy landscape networks of spin-glasses
• Logarithmic growth law in the two-dimensional Ising spin glass state resulting from the electron doping in single-layered manganites
• Persistence and Memory in Patchwork Dynamics for Glassy Models
• Scaling of the largest dynamical barrier in the one-dimensional long-range Ising spin-glass
• Non-equilibrium dynamics of polymers and interfaces in random media : conjecture $\psi =d_s/2$ for the barrier exponent