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arXiv:cond-mat/9303025

Study of +/-J Ising Spin Glasses via Multicanonical Ensemble

Tarık Çelik, Ulrich H. E. Hansmann, Bernd A. Berg

Published Mar 13, 1993• 0 citations
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Abstract

We performed numerical simulations of 2D and 3D Edwards-Anderson spin glass models by using the recently developed multicanonical ensemble. Our ergodicity times increase with the lattice size approximately as $V^3$. The energy, entropy and other physical quantities are easily calculable at all temperatures from a single simulation. Their finite size scalings and the zero temperature limits are also explored.

DOI
10.48550/arxiv.cond-mat/9303025

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We performed numerical simulations of 2D and 3D Edwards-Anderson spin glass models by using the recently developed multicanonical ensemble. Our ergodicity times increase with the lattice size approximately as V3V^3V3. The energy, entropy and other physical quantities are easily calculable at all temperatures from a single simulation. Their finite size scalings and the zero temperature limits are also explored.
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Critical behavior of Ising spin-glass with $\ifmmode\pm\else\textpm\fi{}J$ distribution is discussed. The results are based on the high-temperature series expansion of Edwards-Anderson susceptibility in powers of w(=tanh2JkT)w (=\frac{{tanh}^{2}J}{\mathrm{kT}})w(=kTtanh2J​) for 2D, 3D, and 4D "cubic" lattices to orders 19, 17, and 15, respectively. The lengths of the series are comparable to the best available for the pure Ising model. While 3D and 4D systems exhibit transitions at finite temperatures, in 2D a zero-temperature transition with a power-law divergence (in inverse temperature) for the susceptibility is found. The estimates of critical temperatures and exponents are presented.
We report a high-precision finite-size scaling study of the critical behavior of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass). We have thermalized lattices up to L=40L=40L=40 using the Janus dedicated computer. Our analysis takes into account leading-order corrections to scaling. We obtain Tc=1.1019(29){T}_{\mathrm{c}}=1.1019(29)Tc​=1.1019(29) for the critical temperature, $\ensuremath{\nu}=2.562(42)$ for the thermal exponent, $\ensuremath{\eta}=\ensuremath{-}0.3900(36)$ for the anomalous dimension, and $\ensuremath{\omega}=1.12(10)$ for the exponent of the leading corrections to scaling. Standard (hyper)scaling relations yield $\ensuremath{\alpha}=\ensuremath{-}5.69(13)$, $\ensuremath{\beta}=0.782(10)$, and $\ensuremath{\gamma}=6.13(11)$. We also compute several universal quantities at Tc{T}_{\mathrm{c}}Tc​.
Numerical studies of a compressible version of the Ising spin glass in two dimensions are reported. Compressibility is introduced by adding a term that couples the spin-spin interactions and local lattice deformations to the standard Edwards-Anderson model. The relative strength of this coupling is controlled by a single dimensionless parameter $\ensuremath{\mu}$. The time scale associated with the dynamics of the system grows exponentially as $\ensuremath{\mu}$ is increased, and the energy of the compressible system is shifted downward by an amount proportional to $\ensuremath{\mu}$ times the square of the uncoupled energy. This result leads to the formulation of a simplified model that depends solely on spin variables; analysis and numerical simulations of the simplified model predict a critical value of the coupling strength above which the spin-glass transition cannot exist at any temperature.