Universal Short-Time Dynamics in the Kosterlitz-Thouless Phase

Details Universal Short-Time Dynamics in the Kosterlitz-Thouless Phase Universal Short-Time Dynamics in the Kosterlitz-Thouless Phase

1995-10-13

arxiv.org/abs/cond-mat/9510078v1

Phys. Rev. E 53 (1996) 3333

Physics

Condensed Matter

16 pages, 9 postscript figures, REVTEX 3.0, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.53.3333

We study the short-time dynamics of systems that develop ``quasi long-range order'' after a quench to the Kosterlitz-Thouless phase. With the working hypothesis that the ``universal short-time behavior'', previously found in Ising-like systems, also occurs in the Kosterlitz-Thouless phase, we explore the scaling behavior of thermodynamic variables during the relaxational process following the quench. As a concrete example, we investigate the two-dimensional $6$-state clock model by Monte Carlo simulation. The exponents governing the magnetization, the second moment, and the autocorrelation function are calculated. From them, by means of scaling relations, estimates for the equilibrium exponents $z$ and $\eta$ are derived. In particular, our estimates for the temperature-dependent anomalous dimension $\eta$ that governs the static correlation function are consistent with existing analytical and numerical results and, thus, confirm our working hypothesis.

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