The 3d Ising Model represented as Random Surfaces

TL;DR

This paper introduces a novel random surface representation of the 3D Ising model, revealing scaling behavior and a new critical index that connects string theory parameters to the model's specific heat exponent, determined through simulations.

Contribution

It proposes a new surface-based representation of the 3D Ising model and introduces a critical index linking string theory and statistical physics, explored via numerical simulations.

Findings

Identification of a new critical index $$ relating string and Ising exponents

Evidence of scaling behavior in the random surface representation

Numerical estimation of the critical index $$

Abstract

We consider a random surface representation of the three-dimensional Ising model.The model exhibit scaling behaviour and a new critical index $\k$ which relates $\g_{string}$ for the bosonic string to the exponent $\a$ of the specific heat of the 3d Ising model is introduced. We try to determine $\k$ by numerical simulations.