Two and Three-Dimensional Spin Systems with Gonihedric Action

TL;DR

This paper investigates 2D and 3D spin systems with gonihedric action through numerical simulations, revealing a second order phase transition in 3D that aligns with 2D Ising model results, and proposes order parameters for vacuum states.

Contribution

It provides numerical evidence of phase transitions in gonihedric spin systems and introduces order parameters to characterize vacuum structures and phase behavior.

Findings

Second order phase transition observed in 3D system at β ≈ 0.43932

Transition temperature nearly matches 2D Ising model

Degeneracy of vacuum states quantified for lattice sizes

Abstract

We perform numerical simulations of the two and three-dimensional spin systems with competing interaction. They describe the model of random surfaces with linear-gonihedric action.The degeneracy of the vacuum state of this spin system is equal to $~~d \cdot 2^{N}~~$ for the lattice of the size $~N^{d}~$. We observe the second order phase transition of the three-dimensional system, at temperature $\beta_{c} \simeq 0.43932$ which almost coincides with $\beta_{c}$ of the 2D Ising model. This confirms the earlier analytical result for the case when self-interaction coupling constant $k$ is equal to zero. We suggest the full set of order parameters which characterize the structure of the vacuum states and of the phase transition.