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Dynamics of the two-dimensional gonihedric spin model
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In this paper, we study dynamical aspects of the two-dimensional (2D) 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 ¿. The ¿=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 allowing for ¿¿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 nonglassy evolution (unlike its 3D counterpart). We find, also in this ¿=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 approach to equilibrium has been found.
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ESPRIU, D. (domènec), PRATS FERRER, Aleix. Dynamics of the two-dimensional gonihedric spin model. _Physical Review E_. 2004. Vol. 70, núm. 4, pàgs. 046117. [consulta: 24 de gener de 2026]. ISSN: 1539-3755. [Disponible a: https://hdl.handle.net/2445/18724]