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arXiv:cond-mat/9609232

Comment on ``Generalized Dynamic Scaling for Critical Relaxation" [Phys. Rev. Lett. 77, 679 (1996), cond-mat/9607013]

Uwe Ritschel, Peter Czerner

Published Sep 24, 1996• 0 citations
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Abstract

We point out that in nonequilibrium relaxational processes the magnetic field of the initial state (instead of the initial magnetization) has to be considered as the additional scaling field (related to the initial state). Taking this into account the interpretation of the scaling behavior observed in the paper by Zheng becomes more straightforward.

DOI
10.48550/arxiv.cond-mat/9609232

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We point out that in nonequilibrium relaxational processes the magnetic field of the initial state (instead of the initial magnetization) has to be considered as the additional scaling field (related to the initial state). Taking this into account the interpretation of the scaling behavior observed in the paper by Zheng becomes more straightforward.
In a section of a recent paper [Phys. Rev. B 91, 104432 (2015)], the authors discuss some of the arguments in the paper by Parisi and Temesv\'ari [Nucl. Phys. B 858, 293 (2012)]. In this Comment, it is shown how these arguments are misinterpreted and the existence of the Almeida-Thouless transition in\mathit{in}in the upper critical dimension six reasserted.
We reply to the comment on our published paper `` Universal Fluctuations in Correlated Systems'',Phys. Rev. Lett. Vol; 84, p3744 (2000), by B. Zheng and S. Trimper, cond-mat/0109003. We argue that their results confirm our conjecture, that the probability distribution for order parameter fluctuations in the 2D and 3D Ising models at a temperature T∗(L)T^{\ast}(L)T∗(L) slightly below TCT_CTC​ for the infinite, system approximates the universal functional form of the 2D-XY model in its low temperature phase. We discuss the relevance of the temperature interval TC−T∗T_C-T^{\ast}TC​−T∗, considered to be large by Zheng and Trimper and explain why the observed phenomena is a critical phenomena.
We reconsider the random bond antiferromagnetic spin-1/2 chain for weak disorder and demonstrate the existence of crossover length scale x_W that diverges with decreasing strength of the disorder. Recent DMRG calculations [Phys. Rev. Lett. 89, 127202 (2002); cond-mat/0111027] claimed to have found evidence for a non-universal behavior in this model and found no indications of a universal infinite randomness fixed point (IRFP) scenario. We show that these data are not in the asymptotic regime since the system sizes that have been considered are of the same order of magnitude or much smaller than the crossover length x_W. We give a scaling form for the xx-spin-correlation function that takes this crossover length into account and that is compatible with the IRFP scenario and a random singlet phase.