Dynamical Critical Properties of the Random-Bond three-state Potts Model
Abstract
We study the dynamic critical behavior of the two-dimensional random-bond three-state Potts model using large-scale Monte Carlo simulations with the Wolff and Swendsen--Wang cluster algorithms. At the disorder-dependent critical temperature, we compute integrated and exponential autocorrelation times and extract the dynamic critical exponent z via finite-size scaling. Critical slowing down is significantly weakened by bond randomness, with the dynamic exponent decreasing from z ≈ 0.54 in the pure system to z ≈ 0.24 at strong disorder. From the finite-size scaling of the Wolff cluster size, we obtain γ/ν≈ 1.73, where γ and ν are the susceptibility and correlation-length exponents, respectively, consistent with the universality class of the two-dimensional three-state Potts model. These results indicate that bond randomness strongly affects the critical dynamics but leaves the underlying static universality class unchanged. Furthermore, both static and dynamic observables, including the specific heat and the autocorrelation times, show a lack of self-averaging.
Versions
Related
- Dynamical Phase Transitions as Properties of the Stationary State: Analytic Results after Quantum Quenches in the Spin-1/2 XXZ Chain
- Spectral and steady-state properties of fermionic random quadratic Liouvillians
- Effective-Geometry Rescaling and Universal Critical Behavior in the Anisotropic Three-State Potts Model on the Square Lattice
- Dynamical and structural properties of an absorbing phase transition: a case study from granular systems
- Exploring Dynamical Quantum Phase Transitions via the Dynamical Phase Accumulated at an Equilibrium Critical Point
BibTeX
@misc{vatansever2026dynamical,
title = {{Dynamical Critical Properties of the Random-Bond three-state Potts Model}},
author = {Zeynep Demir Vatansever and Ulvi Kanbur and Mohammed Sadra Najafi and Muktish Acharyya and Erol Vatansever},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01176},
eprint = {2610.01176},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01176},
note = {CC0},
}
RIS
TY - UNPB
TI - Dynamical Critical Properties of the Random-Bond three-state Potts Model
AU - Zeynep Demir Vatansever
AU - Ulvi Kanbur
AU - Mohammed Sadra Najafi
AU - Muktish Acharyya
AU - Erol Vatansever
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01176
UR - https://arxiv.org/abs/2610.01176
AB - We study the dynamic critical behavior of the two-dimensional random-bond three-state Potts model using large-scale Monte Carlo simulations with the Wolff and Swendsen--Wang cluster algorithms. At the disorder-dependent critical temperature, we compute integrated and exponential autocorrelation times and extract the dynamic critical exponent z via finite-size scaling. Critical slowing down is significantly weakened by bond randomness, with the dynamic exponent decreasing from z ≈ 0.54 in the pure system to z ≈ 0.24 at strong disorder. From the finite-size scaling of the Wolff cluster size, we obtain γ/ν≈ 1.73, where γ and ν are the susceptibility and correlation-length exponents, respectively, consistent with the universality class of the two-dimensional three-state Potts model. These results indicate that bond randomness strongly affects the critical dynamics but leaves the underlying static universality class unchanged. Furthermore, both static and dynamic observables, including the specific heat and the autocorrelation times, show a lack of self-averaging.
ER -