Loop transfer matrix and gonihedric loop diffusion

TL;DR

This paper analyzes a 3D gonihedric system using a transfer matrix approach, deriving its exact partition function and critical indices, and reveals a connection to the 2D Ising model.

Contribution

It provides the exact partition function and critical indices for a 3D gonihedric system and elucidates its relation to the 2D Ising model.

Findings

Exact partition function of the 3D gonihedric model derived

Critical indices analyzed via transfer matrix

Connection between 3D gonihedric system and 2D Ising model established

Abstract

We study a class of statistical systems which simulate 3D gonihedric system on euclidean lattice. We have found the exact partition function of the 3D-model and the corresponding critical indices analysing the transfer matrix $K(P_{i},P_{f})$ which describes the propagation of loops on a lattice. The connection between 3D gonihedric system and 2D-Ising model is clearly seen.