# Phase Transition in Lattice Surface Systems with Gonihedric Action

## TL;DR

This paper proves the existence of an ordered phase in a lattice surface model with gonihedric action, extending Peierls contour methods to surfaces based on curvature and contact interactions.

## Contribution

It introduces a rigorous proof of phase transition in a lattice gonihedric surface model, advancing understanding of random surface behavior with curvature-dependent weights.

## Key findings

- Existence of an ordered low-temperature phase confirmed.
- Extension of Peierls contour method to surface models.
- Model captures curvature and contact interactions in surface configurations.

## Abstract

We prove the existence of an ordered low temperature phase in a model of soft-self-avoiding closed random surfaces on a cubic lattice by a suitable extension of Peierls contour method. The statistical weight of each surface configuration depends only on the mean extrinsic curvature and on an interaction term arising when two surfaces touch each other along some contour. The model was introduced by F.J. Wegner and G.K. Savvidy as a lattice version of the gonihedric string, which is an action for triangulated random surfaces.