Dynamics of the two-dimensional gonihedric spin model

Area of Science:

• Statistical mechanics
• Condensed matter physics
• Computational physics

Background:

• The gonihedric spin model describes an ensemble of loops on a 2D surface with vanishing microscopic surface tension.
• The behavior of this model is influenced by loop self-avoidance, parameterized by kappa.
• Previous studies indicated the kappa=0 case lacks critical behavior.

Purpose of the Study:

• To investigate the dynamical aspects of the two-dimensional gonihedric spin model.
• To determine if loop self-avoidance (kappa != 0) induces critical behavior.
• To analyze finite-size effects and understand the system's long-time evolution.

Main Methods:

• Numerical simulations
• Analytical calculations
• Finite-volume calculations for non-self-avoiding loops
• Dual description in terms of defects

Main Results:

• The model does not exhibit critical behavior for any value of kappa.
• Finite-size effects are significant and were analyzed.
• The system displays very slow dynamics but demonstrates non-glassy evolution, unlike its 3D counterpart.
• A power law, not logarithmic, governs the approach to equilibrium at long times and low temperatures.

Conclusions:

• The two-dimensional gonihedric spin model lacks critical behavior, irrespective of loop self-avoidance.
• The model's slow dynamics are characterized by non-glassy evolution and a power-law approach to equilibrium.
• A dual description using defects provides insights into the system's long-time behavior.