Universal Short-Time Dynamics in the Kosterlitz-Thouless Phase

TL;DR

This paper investigates the universal short-time dynamic scaling behavior in the Kosterlitz-Thouless phase, using Monte Carlo simulations of the 2D 6-state clock model to estimate critical exponents and confirm universality.

Contribution

It demonstrates that the universal short-time dynamics observed in Ising-like systems also applies to the Kosterlitz-Thouless phase, providing numerical estimates of critical exponents.

Findings

Estimated critical exponents match existing analytical results.

Confirmed the universality of short-time dynamics in the Kosterlitz-Thouless phase.

Validated the scaling relations for dynamic variables.

Abstract

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.