2003/12/31 by D. Espriu, Alberto Prats‐Galino, A. Prats
Materials Science · Mathematics · Physics and Astronomy · #Combinatorics #Logarithm #Material Dynamics and Properties #Mathematical analysis #Mathematics #Observable #Physics #Power law #Quantum many-body systems #Quantum mechanics #Spin (aerodynamics) #Spin model #Statistical physics #Theoretical and Computational Physics #Thermodynamics #Vertex (graph theory) #cond-mat.soft #cond-mat.stat-mech #hep-lat
paper · pdf · doi:10.1103/physreve.70.046117
published as Phys.Rev. E70 (2004) 046117 · 23 pages, 17 figures, UB-ECM-PF-03/38
openalex publication_date 2004/10/01 · arxiv created 2005/11/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 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 allowing for kappa not equal 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 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 approach to equilibrium has been found.