Dynamics of the two-dimensional gonihedric spin model

Abstract

In this paper we study dynamical aspects of the two-dimensional gonihedric spin model using both numerical and analytical methods. This spin model has vanishing microscopic surface tension and it actually describes an ensemble of loops living on a 2D surface. The self-avoidance of loops is parametrized by a parameter $\kappa$. The $\kappa =0$ model can be mapped to one of the six-vertex models discussed by Baxter and it does not have critical behavior. We have found that $\kappa \ne 0$ does not lead to critical behavior either. Finite size effects are rather severe, and in order to understand these effects a finite volume calculation for non self-avoiding loops is presented. This model, like his 3D counterpart, exhibits very slow dynamics, but a careful analysis of dynamical observables reveals non-glassy evolution (unlike its 3D counterpart). We find, also in this $\kappa =0$ case, the law that governs the long-time, low-temperature evolution of the system, through a dual description in terms of defects. A power, rather than logarithmic, law for the approximation to equilibrium has been found.

23 pages, 17 figures, UB-ECM-PF-03/38

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• Fracton-like phases from subsystem symmetries
• Fracton excitations in classical frustrated kagome spin models
• Glassy behaviour in an exactly solved spin system with a ferromagnetic transition
• Mixing length scales of low temperature spin plaquettes models
• On gonihedric loops and quantum gravity
• Frustrated Ising model on the honeycomb lattice: Metastability and universality