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arXiv:cond-mat/0702302 · Physical Review Letters

Scaling Analysis of Domain-Wall Free Energy in the Edwards-Anderson Ising Spin Glass in a Magnetic Field

M. Sasaki, Koji Hukushima, Hajime Yoshino, Hajime Takayama

Published Sep 25, 2007• 24 citations
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Abstract

The stability of the spin-glass phase against a magnetic field is studied in the three- and four-dimensional Edwards-Anderson Ising spin glasses. Effective couplings J(eff) and effective fields H(eff) associated with length scale L are measured by a numerical domain-wall renormalization-group method. The results obtained by scaling analysis of the data strongly indicate the existence of a crossover length beyond which the spin-glass order is destroyed by field H. The crossover length well obeys a power law of H which diverges as H --> 0 but remains finite for any nonzero H, implying that the spin-glass phase is absent even in an infinitesimal field. These results are well consistent with the droplet theory for short-range spin glasses.

DOI
10.1103/physrevlett.99.137202

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Spin-glass (SG) states of the 3-dimensional Ising Edwards-Anderson model under a static magnetic field hhh are examined by means of the standard Monte Carlo simulation on the field-shift aging protocol at temperature TTT. For each process with $(T; \tw, h)$, $\tw$ being the waiting time before the field is switched on, we extract the dynamical crossover time, $\tcr(T; \tw, h)$. We have found a nice scaling relation between the two characteristic length scales which are properly determined from $\tcr$ and $\tw$ and then are normalized by the static field crossover length introduced in the SG droplet theory. This scaling behavior implies the instability of the SG phase in the equilibrium limit even under an infinitesimal hhh. In comparison with this numerical result the field effect on real spin glasses is also discussed.
We present numerical simulations of the four-dimensional Edwards Anderson Ising spin glass with binary couplings. Our results, in the midst of strong finite-size effects, suggest the existence of a spin-glass phase transition. We present a preliminar determination of critical exponents. We discuss spin-glass susceptibilities, cumulants of the overlap and energy overlap probability distributions, finite-size effects, and the behaviour of the disorder-dependent and integrated probability distributions.
The distribution of energy and free energy of domain walls near the spin-glass transition is studied numerically in the three-dimensional Ising spin-glass model with discrete $\ifmmode\pm\else\textpm\fi{}J$ interactions. Temperature dependence of the width of the free-energy distribution clearly shows a phase transition to a low-temperature phase with long-range spin correlations at $\frac{k{T}_{g}}{J}\ensuremath{\simeq}1.2$. Simple scaling analysis is consistent with previous studies of this system.
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