Fixed boundary conditions analysis of the 3d Gonihedric Ising model with $\kappa=0$

TL;DR

This paper conducts a high-statistics analysis of the 3D Gonihedric Ising model with fixed boundary conditions, precisely identifying the first order phase transition point and validating scaling laws for relevant observables.

Contribution

It provides the first precise determination of the transition inverse temperature and confirms the applicability of scaling laws to fixed boundary conditions in this model.

Findings

Transition inverse temperature at β_c = 0.54757(63)

Validation of scaling laws for first order transitions with fixed boundaries

Evidence supporting the first order nature of the phase transition

Abstract

The Gonihedric Ising model is a particular case of the class of models defined by Savvidy and Wegner intended as discrete versions of string theories on cubic lattices. In this paper we perform a high statistics analysis of the phase transition exhibited by the 3d Gonihedric Ising model with $k=0$ in the light of a set of recently stated scaling laws applicable to first order phase transitions with fixed boundary conditions. Even though qualitative evidence was presented in a previous paper to support the existence of a first order phase transition at $k=0$, only now are we capable of pinpointing the transition inverse temperature at $\beta_c = 0.54757(63)$ and of checking the scaling of standard observables.