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Bulletin of the American Physical Society

Typical Value of Susceptibilities in the Three Dimensional Edwards-Anderson Spin Glass Model in an External Field

Sheng Feng, Ka-Ming Tam, Fang Ye, Jagannathan Ramanujam, Juana Moreno, Mark Jarrell

Published Mar 3, 2015• 0 citations
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The three-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied via large-scale Monte Carlo simulations at low temperatures, deep within the spin-glass phase. Performing a careful statistical analysis of several thousand independent disorder realizations and using an observable that detects peaks in the overlap distribution, we show that the Sherrington-Kirkpatrick and Edwards-Anderson models have a distinctly different low-temperature behavior. The structure of the spin-glass overlap distribution for the Edwards-Anderson model suggests that its low-temperature phase has only a single pair of pure states.
We present a replica derivation for the claim that the averaged square of the local spin expectation value in the long-range spin glass model is equal to the minimum, q(0) of Parisi's order parameters q(x). This corresponds to the dynamic interpretation of q(x) due to Sompolinsky. We show that q(0) obeys a power law q(0) ∼ b 2/3 for low external fields b and all temperatures 0 < T < Tc. Furthermore we calculate the low field magnetization for all temperatures. The calculations are based on an exact relation for the renormalized local susceptibility which replaces the Parisi-Toulouse hypothesis.