Four-dimensional gonihedric gauge spin system

TL;DR

This paper investigates a four-dimensional gauge invariant spin system modeling random surfaces with gonihedric action, revealing phase transition analogies with liquid-gas systems through Monte Carlo simulations.

Contribution

It introduces a novel analogy between the flat-crumpled phase transition of lattice surfaces and liquid-gas transitions, linking the self-intersection coupling to pressure.

Findings

Identified critical points analogous to liquid-gas phase transitions.

Measured vacuum expectation values and critical indices.

Established the role of the self-intersection coupling constant.

Abstract

We perform Monte Carlo simulations of a four-dimensional gauge invariant spin system which describes random surfaces with gonihedric action. We develop the analogy between the flat-crumpled phase transition of the lattice surface model and the liquid-gas phase transition of non-ideal gases, and identify the self-intersection coupling constant $k$ of the surface model with the pressure $P$. As $k$ increases the system moves to a critical point in complete analogy with the situation for non-ideal gases, where the liquid and the gas phases approach each other with increasing $P$. We measure vacuum expectation values of various operators and the corresponding critical indices.