Self-Avoiding Gonihedric Srting and Spin Systems

TL;DR

This paper classifies theories of self-intersecting random surfaces with varying intersection weights, constructs equivalent spin systems, and analyzes their disorder properties, especially in two dimensions.

Contribution

It introduces a classification of self-intersecting surface theories and constructs equivalent spin systems, exploring their behavior across different intersection couplings.

Findings

Surface theories range from freely intersecting to completely self-avoiding as 2 varies.

Equivalent spin systems are constructed for the general case.

In 2D, the 2=0 system exhibits complete disorder, similar to 2D gauge Ising.

Abstract

We classify different theories of self-intersecting random surfaces assigning special weights to intersections. When self-intersection coupling constant $\kappa$ tends to zero, then the surface can freely inetrsect and it is completely self-avoiding when $\kappa$ tends to infinity. Equivalent spin systems for this general case were constructed. In two-dimension the system with $\kappa = 0$ is in complete disorder as it is in the case of 2D gauge Ising system.