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• W4307285417 abstract "Abstract We revisit the Haake–Lewenstein–Wilkens approach to Edwards–Anderson (EA) model of Ising spin glass (SG) (Haake et al 1985 Phys. Rev. Lett. 55 2606). This approach consists in evaluation and analysis of the probability distribution of configurations of two replicas of the system, averaged over quenched disorder. This probability distribution generates squares of thermal copies of spin variables from the two copies of the systems, averaged over disorder, that is the terms that enter the standard definition of the original EA order parameter, <?CDATA $q_textrm{EA}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mi>q</mml:mi> <mml:mrow> <mml:mtext>EA</mml:mtext> </mml:mrow> </mml:msub> </mml:math> . We use saddle point/steepest descent (SPSD) method to calculate the average of the Gaussian disorder in higher dimensions. This approximate result suggest that <?CDATA $q_textrm{EA}gt 0$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mi>q</mml:mi> <mml:mrow> <mml:mtext>EA</mml:mtext> </mml:mrow> </mml:msub> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:math> at <?CDATA $0lt Tlt T_c$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mn>0</mml:mn> <mml:mo><</mml:mo> <mml:mi>T</mml:mi> <mml:mo><</mml:mo> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> in 3D and 4D. The case of 2D seems to be a little more subtle, since in the present approach energy increase for a domain wall competes with boundary/edge effects more strongly in 2D; still our approach predicts SG order at sufficiently low temperature. We speculate, how these predictions confirm/contradict widely spread opinions that: (i) There exist only one (up to the spin flip) ground state in EA model in 2D, 3D and 4D; (ii) there is (no) SG transition in 3D and 4D (2D). This paper is dedicated to the memories of Fritz Haake and Marek Cieplak." @default.
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• W4307285417 date "2022-11-11" @default.
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• W4307285417 title "Haake–Lewenstein–Wilkens approach to spin-glasses revisited" @default.
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• W4307285417 doi "https://doi.org/10.1088/1751-8121/ac9d10" @default.
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