Interaction Hierarchy

TL;DR

This paper introduces a new class of statistical lattice systems based on a hierarchy of energy functionals, revealing connections to 2D Ising fermions and proposing a dual system with novel spin variables.

Contribution

It develops a hierarchical framework for statistical surface systems and establishes their equivalence to free fermion propagation, introducing a new dual spin system.

Findings

Hierarchical structure of energy functionals influences surface dynamics and phase transitions.

3D gonihedric system is equivalent to free 2D Ising fermions.

A dual statistical system with matchbox spin variables is constructed.

Abstract

We analyse a new class of statistical systems, which simulate different systems of random surfaces on a lattice. Geometrical hierarchy of the energy functionals on which these theories are based produces corresponding hierarchy of the surface dynamics and of the phase transitions. We specially consider 3D gonihedric system and have found that it is equivalent to the propagation of almost free 2D Ising fermions. We construct dual statistical system with new matchbox spin variable $G_{\xi}$, high temperature expansion of which equally well describe these surfaces.