Nonuniversality in short-time critical dynamics

TL;DR

This study investigates how the dynamical critical exponents of the 2D Ising model with a defect line vary with defect strength, revealing nonuniversality in some exponents but not others during early-time dynamics.

Contribution

It demonstrates that certain critical exponents depend on defect strength, while others remain invariant, highlighting nuanced behavior in short-time critical dynamics.

Findings

Critical exponent of Janssen et al depends on defect strength J'

Dynamical critical exponent z is insensitive to J'

Anomalous dimension of magnetization may be invariant

Abstract

We study behaviour of dynamical critical exponents of the two-dimensional Ising model with a line of defects. Simulations done at an early time (first 100 Monte Carlo steps) reveal that the critical exponent of Janssen et al (Z. Phys. B 73 539) depends on the strength of the exchange coupling constant (J') of the altered line. On the other hand, our simulations permit us to conclude that the dynamical critical exponent z is not sensitive to changes in J'. In adition, we investigate the possible invariance of the anomalous dimension of the magnetization at the beginning of the process.