Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0207123

Eigenmode analysis of the susceptibility matrix of the four-dimensional Edwards-Anderson spin-glass model

Koji Hukushima, Yukito Iba

Published Jul 4, 2002• 0 citations
arXivHTMLPDF

Abstract

The nature of spin-glass phase of the four-dimensional Edwards-Anderson Ising model is numerically studied by eigenmode analysis of the susceptibility matrix up to the lattice size 10^4. Unlike the preceding results on smaller lattices, our result suggests that there exist multiple extensive eigenvalues of the matrix, which does not contradict replica-symmetry-breaking scenarios. The sensitivity of the eigenmodes with respect to a temperature change is examined using finite-size-scaling analysis and an evidence of anomalous sensitivity is found. A computational advantage of dual formulation of the eigenmode analysis in the study of large lattices is also discussed.

DOI
10.48550/arxiv.cond-mat/0207123

Related papers

Eigenvalue analysis of the density matrix of four-dimensional spin glasses supports replica symmetry breaking

Lorenzo Correale, Enzo Marinari, Víctor Martín-Mayor

We present a general and powerful numerical method useful to study the density matrix of spin models. We apply the method to finite-dimensional spin glasses, and analyze in detail the four-dimensional Edwards-Anderson model with Gaussian quenched random couplings. Our results clearly support the existence of replica symmetry breaking in the thermodynamical limit.

arXiv:cond-mat/0207460•Physical review. B, Condensed matter•Nov 4, 2002•2 citations

Numerical simulations of the four-dimensional Edwards-Anderson spin glass with binary couplings

Enzo Marinari, Francesco Zuliani

We present numerical results that allow a precise determination of the transition point and of the critical exponents of the four-dimensional Edwards-Anderson spin glass with binary quenched random couplings. We show that the low-temperature phase undergoes replica symmetry breaking. We obtain results on large lattices, up to a volume V = 10 4 : we use finite-size scaling to show the relevance of our results in the infinite volume limit.

arXiv:cond-mat/9904303•Journal of Physics A Mathematical and General•Oct 13, 1999•36 citations

Phase structure of the three-dimensional Edwards-Anderson spin glass

Enzo Marinari, Giorgio Parisi A, Juan Jesus Ruiz-Lorenzo

We characterize numerically the properties of the phase transition of the three-dimensional Ising spin glass with Gaussian couplings and of the low-temperature phase. We compute critical exponents on large lattices. We study in detail the overlap probability distribution and the equilibrium overlap-overlap correlation functions. We find a clear agreement with off-equilibrium results from previous work. These results strongly support the existence of a continuous spontaneous replica symmetry breaking in three-dimensional spin glasses.

arXiv:cond-mat/9802211•Physical review. B, Condensed matter•Dec 1, 1998•108 citations

Critical parameters of the three-dimensional Ising spin glass

Marco Baity‐Jesi, R. A. Baños, Andrés De la Cruz +21 more

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 $L=40$ using the Janus dedicated computer. Our analysis takes into account leading-order corrections to scaling. We obtain ${T}_{\mathrm{c}}=1.1019(29)$ 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 ${T}_{\mathrm{c}}$.

arXiv:1310.2910•Physical Review B•Dec 20, 2013•116 citations

Extensive eigenvalues in spin-spin correlations: A tool for counting pure states in Ising spin glasses

Jairo Sinova, Geoffrey Canright, Horacio E. Castillo +1 more

We study the nature of the broken ergodicity in the low temperature phase of Ising spin glass systems, using as a diagnostic tool the spectrum of eigenvalues of the spin-spin correlation function. We show that multiple extensive eigenvalues of the correlation matrix ${C}_{\mathrm{ij}}\ensuremath{\equiv}〈{S}_{i}{S}_{j}〉$ occur if and only if there is replica symmetry breaking. We support our arguments with Exchange Monte Carlo results for the infinite-range problem. Here we find multiple extensive eigenvalues in the replica symmetry breaking (RSB) phase for $N\ensuremath{\gtrsim}200,$ but only a single extensive eigenvalue for phases with long-range order but no RSB. Numerical results for the short-range model in four spatial dimensions, for $N<~1296,$ are consistent with the presence of a single extensive eigenvalue, with the subdominant eigenvalue behaving in agreement with expectations derived from the droplet model. Because of the small system sizes we cannot exclude the possibility of replica symmetry breaking with finite size corrections in this regime.

arXiv:cond-mat/0010302•Physical review. B, Condensed matter•Feb 20, 2001•12 citations

Critical behaviour of the four-dimensional spin glass in magnetic field

Enzo Marinari, C. Naitza, Francesco Zuliani

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.

arXiv:cond-mat/9802224•Journal of Physics A Mathematical and General•Jul 31, 1998•25 citations
The nature of spin-glass phase of the four-dimensional Edwards-Anderson Ising model is numerically studied by eigenmode analysis of the susceptibility matrix up to the lattice size 10^4. Unlike the preceding results on smaller lattices, our result suggests that there exist multiple extensive eigenvalues of the matrix, which does not contradict replica-symmetry-breaking scenarios. The sensitivity of the eigenmodes with respect to a temperature change is examined using finite-size-scaling analysis and an evidence of anomalous sensitivity is found. A computational advantage of dual formulation of the eigenmode analysis in the study of large lattices is also discussed.
We characterize numerically the properties of the phase transition of the three-dimensional Ising spin glass with Gaussian couplings and of the low-temperature phase. We compute critical exponents on large lattices. We study in detail the overlap probability distribution and the equilibrium overlap-overlap correlation functions. We find a clear agreement with off-equilibrium results from previous work. These results strongly support the existence of a continuous spontaneous replica symmetry breaking in three-dimensional spin glasses.
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​.
We study the nature of the broken ergodicity in the low temperature phase of Ising spin glass systems, using as a diagnostic tool the spectrum of eigenvalues of the spin-spin correlation function. We show that multiple extensive eigenvalues of the correlation matrix ${C}_{\mathrm{ij}}\ensuremath{\equiv}〈{S}_{i}{S}_{j}〉$ occur if and only if there is replica symmetry breaking. We support our arguments with Exchange Monte Carlo results for the infinite-range problem. Here we find multiple extensive eigenvalues in the replica symmetry breaking (RSB) phase for $N\ensuremath{\gtrsim}200,$ but only a single extensive eigenvalue for phases with long-range order but no RSB. Numerical results for the short-range model in four spatial dimensions, for N< 1296,N<~1296,N< 1296, are consistent with the presence of a single extensive eigenvalue, with the subdominant eigenvalue behaving in agreement with expectations derived from the droplet model. Because of the small system sizes we cannot exclude the possibility of replica symmetry breaking with finite size corrections in this regime.
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.