Slow dynamics in the 3--D gonihedric model

TL;DR

This paper investigates the slow and glassy dynamics of the 3D gonihedric spin model using Monte Carlo simulations, revealing distinct regimes below a critical temperature and analyzing phase transition behaviors.

Contribution

It provides the first detailed analysis of slow dynamics and glassy behavior in the 3D gonihedric model across different parameter regimes.

Findings

Slow logarithmic dynamics below a glass transition temperature.

Identification of a supercooled phase with metastability.

Presence of glassy behavior and aging phenomena below the critical temperature.

Abstract

We study dynamical aspects of three--dimensional gonihedric spins by using Monte--Carlo methods. The interest of this family of models (parametrized by one self-avoidance parameter $\kappa$) lies in their capability to show remarkably slow dynamics and seemingly glassy behaviour below a certain temperature $T_g$ without the need of introducing disorder of any kind. We consider first a hamiltonian that takes into account only a four--spin term ($\kappa=0$), where a first order phase transition is well established. By studying the relaxation properties at low temperatures we confirm that the model exhibits two distinct regimes. For $T_g< T < T_c$, with long lived metastability and a supercooled phase, the approach to equilibrium is well described by a stretched exponential. For $T<T_g$ the dynamics appears to be logarithmic. We provide an accurate determination of $T_g$. We also determine the evolution of particularly long lived configurations. Next, we consider the case $\kappa=1$, where the plaquette term is absent and the gonihedric action consists in a ferromagnetic Ising with fine-tuned next-to-nearest neighbour interactions. This model exhibits a second order phase transition. The consideration of the relaxation time for configurations in the cold phase reveals the presence of slow dynamics and glassy behaviour for any $T< T_c$. Type II aging features are exhibited by this model.