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arXiv:cond-mat/0208380 · Physical Review Letters

Comment on “Critical Dynamics of a Vortex-Loop Model for the Superconducting Transition”

Jack Lidmar

Published Aug 15, 2002• 2 citations
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Abstract

Recently, Aji and Goldenfeldt [Phys. Rev. Lett. 87, 197003 (2001), cond-mat/0105622] put forward an explanation for the value of the dynamic critical exponent z observed in certain Monte Carlo simulations of the superconducting phase transition in zero magnetic field. In this Comment, we point out that their analysis is based on incorrect assumptions regarding the scaling dimension of the vortex density.

DOI
10.1103/physrevlett.89.109701

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This is a response to the comment by J. Lidmar on our work in Phys. Rev. Lett. 87, 197003 (2001), cond-mat/0105622. We show explicitly that, contrary to the statements in the comment, our scaling analysis correctly reproduces the Josephson scaling relation and other known theoretical results, and explains the surprising results of dynamic Monte Carlo simulations in 3D for the vortex loop model. Our explanation, being based on identifying the correct relationship between real and Monte Carlo time, is not relevant for static Monte Carlo simulations, whose results do not need correction.

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Critical Dynamics of a Vortex-Loop Model for the Superconducting Transition

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Recently, Aji and Goldenfeldt [Phys. Rev. Lett. 87, 197003 (2001), cond-mat/0105622] put forward an explanation for the value of the dynamic critical exponent z observed in certain Monte Carlo simulations of the superconducting phase transition in zero magnetic field. In this Comment, we point out that their analysis is based on incorrect assumptions regarding the scaling dimension of the vortex density.
This is a response to the comment by J. Lidmar on our work in Phys. Rev. Lett. 87, 197003 (2001), cond-mat/0105622. We show explicitly that, contrary to the statements in the comment, our scaling analysis correctly reproduces the Josephson scaling relation and other known theoretical results, and explains the surprising results of dynamic Monte Carlo simulations in 3D for the vortex loop model. Our explanation, being based on identifying the correct relationship between real and Monte Carlo time, is not relevant for static Monte Carlo simulations, whose results do not need correction.
We calculate analytically the dynamic critical exponent zMC{z}_{\mathrm{MC}}zMC​, measured in Monte Carlo simulations for a vortex loop model of the superconducting transition, and account for the simulation results. In the weak screening limit, where magnetic fluctuations are neglected, the dynamic exponent is found to be zMC=3/2{z}_{\mathrm{MC}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3/2zMC​=3/2. In the perfect screening limit, zMC=5/2{z}_{\mathrm{MC}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5/2zMC​=5/2. We relate zMC{z}_{\mathrm{MC}}zMC​ to the actual value of zzz observable in experiments and find that $z\ensuremath{\sim}2$, consistent with some experimental results.
In the recent study of the Ising model on a small world network by Pekalski [Phys. Rev. E 64, 057104 (2001)], a surprisingly small value of the critical exponent beta approximately 0.0001 has been obtained for the temperature dependence of the magnetization. We perform extensive Monte Carlo simulations of the same model and conclude, via the standard finite-size scaling of various quantities, that the phase transition in the model is of the mean-field nature, in contrast to the work by Pekalski, but in accordance with other existing studies.
In a recent Letter Albano and Saracco study the dynamic critical behavior of some anisotropic driven lattice gases by Monte Carlo (MC) simulations. In this Comment we point out that the Ansätze they use to relate the measured scaling exponents with the critical exponents analytically computed within different field-theoretical approaches do not take properly into account the strongly anisotropic nature of the phase transition, by implicitly assuming z=z⊥=z∥z = z_{\bot} = z_{\parallel}z=z⊥​=z∥​. As a consequence, at variance with the claims by the authors, their MC data are not conclusive to determine which one of the field theories proposed in the literature correctly describes the universal properties of the phase transition in these lattice gases.
In a recent letter, R.G. Brown and M. Ciftan (Phys. Rev. Lett. 76, 1352, 1996) reported high precision Monte Carlo (MC) estimates of the static critical exponents of the classical 3D Heisenberg model, which stand in sharp contrast to values obtained by four independent approaches, namely by other recent high statistics MC simulations, high-temperature series analyses, field theoretical methods, and experimental studies. In reply to the above cited work we submitted this paper as a comment to Phys. Rev. Lett.