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< Domain walls in spin glass
27/07/2018 - Age: 298 days

Discrete or continuous

Model explains degeneracies in spin glasses


A recent study published in Physical Review Letters in collaboration with Mohammad-Sadegh Vaezi and Zohar Nussinov from Washington University, St. Louis, and Gerardo Ortiz from Indiana University, Bloomington, allows us to understand the pronounced differences observed in the ground states of spin glasses with discrete couplings that can cancel each other exactly and continuous distributions where this is not possible. We introduce a new model than interpolates between these extreme cases and derive a rigorous bound for the ground-state entropy.

M.-S. Vaezi, G. Ortiz, M. Weigel, and Z. Nussinov, Binomial Spin Glass, Phys. Rev. Lett. 121, 080601 (2018).

»To establish a unified framework for studying both discrete and continuous coupling distributions, we introduce the binomial spin glass, a class of models where the couplings are sums of m identically distributed Bernoulli random variables. In the continuum limit m -> oo, the class reduces to one with Gaussian couplings, while m=1 corresponds to the +/- J spin glass. We demonstrate that for short-range Ising models on d-dimensional hypercubic lattices the ground-state entropy density for N spins is bounded from above by [(d/2m)1/2 + 1/N] ln2, and further show that the actual entropies follow the scaling behavior implied by this bound. We thus uncover a fundamental non-commutativity of the thermodynamic and continuous coupling limits that leads to the presence or absence of degeneracies depending on the precise way the limits are taken. Exact calculations of defect energies reveal a crossover length scale m* ~ Lκ below which the binomial spin glass is indistinguishable from the Gaussian system. Since κ = -1/2 θ, where θ is the spin-stiffness exponent, discrete couplings become irrelevant at large scales for systems with a finite-temperature spin-glass phase.«