# The Phase Diagram of the Gonihedric 3d Ising Model via CVM

## TL;DR

This paper uses the cluster variation method to analyze the phase diagram of the 3d gonihedric Ising model, revealing its unique phase structure and critical behavior, consistent with Monte Carlo simulations.

## Contribution

It applies the CVM to the gonihedric Ising model, providing insights into its phase transitions and critical exponents, which had not been thoroughly studied before.

## Key findings

- Good agreement with Monte Carlo for critical temperatures
- Determined critical exponent β ≈ 0.062
- Identified phase transition characteristics

## Abstract

We use the cluster variation method (CVM) to investigate the phase structure of the 3d gonihedric Ising actions defined by Savvidy and Wegner. The geometrical spin cluster boundaries in these systems serve as models for the string worldsheets of the gonihedric string embedded in ${\bf Z}^3$. The models are interesting from the statistical mechanical point of view because they have a vanishing bare surface tension. As a result the action depends only on the angles of the discrete surface and not on the area, which is the antithesis of the standard 3d Ising model. The results obtained with the CVM are in good agreement with Monte Carlo simulations for the critical temperatures and the order of the transition as the self-avoidance coupling $\kappa$ is varied. The value of the magnetization critical exponent $\beta = 0.062 \pm 0.003$, calculated with the cluster variation--Pad\`e approximant method, is also close to the simulation results.