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Low-temperature behavior of two-dimensional Gaussian Ising spin glasses

J. Houdayer·Alexander K. Hartmann
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Abstract

We perform Monte Carlo simulations of large two-dimensional Gaussian Ising spin glasses down to very low temperatures $β=1/T=50$. Equilibration is ensured by using a cluster algorithm including Monte Carlo moves consisting of flipping fundamental excitations. We study the thermodynamic behavior using the Binder cumulant, the spin-glass susceptibility, the distribution of overlaps, the overlap with the ground state and the specific heat. We confirm that $T_c=0$. All results are compatible with an algebraic divergence of the correlation length with an exponent $ν$. We find $-1/ν=-0.295(30)$, which is compatible with the value for the domain-wall and droplet exponent $θ\approx-0.29$ found previously in ground-state studies. Hence the thermodynamic behavior of this model seems to be governed by one single exponent.

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J. Houdayer, Alexander K. Hartmann. 2004-02-02. Low-temperature behavior of two-dimensional Gaussian Ising spin glasses. https://doi.org/10.1103/physrevb.70.014418

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