3D-Ising Model as a String Theory in Three Dimentional Euclidean Space

TL;DR

This paper analyzes a 3D string model in strong coupling, revealing a set of models with analytically calculated critical indices that relate to the 3D Ising model and lattice Potts models.

Contribution

It introduces a new set of 3D string models with analytically derived critical indices, linking them to the 3D Ising and Potts models.

Findings

Critical indices depend on two integers (m,n).

A set of models with specific critical behavior is identified.

Connections to 3D lattice Potts models are suggested.

Abstract

A three dimensional string model is analyzed in the strong coupling regime. The contribution of surfaces with different topology to the partition function is essential. A set of corresponding models is discovered. Their critical indices, which depend on two integers (m,n), are calculated analyticaly. The critical indices of the three dimensioal Ising model should belong to this set. A possible connection with the chain of three dimensional lattice Pott's models is pointed out.