# Two and Three-Dimensional Spin Systems with Gonihedric Action

Source: [Two and Three-Dimensional Spin Systems with Gonihedric Action](<https://www.sota2.com/research/paper/68fa31e41e209131ce883261>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T19:09:37.086Z

Authors: G.K.Bathas, E.Floratos, G.K.Savvidy, K.G.Savvidy

Published: 1995-04-10T10:56:37.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/hep-th/9504054>)

[PDF](<https://arxiv.org/pdf/hep-th/9504054.pdf>)