Phase structure of four-dimensional gonihedric spin system

TL;DR

This study uses Monte Carlo simulations to explore the phase transitions of a four-dimensional gonihedric spin system, revealing second-order and first-order transitions and supporting the existence of a noncritical string in four dimensions.

Contribution

It introduces a detailed simulation of a gauge invariant spin system with gonihedric action in four dimensions, highlighting phase transition behaviors and string tension generation.

Findings

Second-order phase transition at $eta_c \,\simeq\, 1.75$ for large $k$

String tension arises from quantum fluctuations

First-order transition for smaller $k$, crossover near zero

Abstract

We perform Monte Carlo simulations of a gauge invariant spin system which describes random surfaces with gonihedric action in four dimensions. The Hamiltonian is a mixture of one-plaquette and additional two- and three-plaquette interaction terms with specially adjusted coupling constants. For the system with the large self-intersection coupling constant $k$ we observe the second-order phase transition at temperature $\beta_{c}\simeq 1.75$. The string tension is generated by quantum fluctuations as it was expected theoretically. This result suggests the existence of a noncritical string in four dimensions. For smaller values of $k$ the system undergoes the first order phase transition and for $k$ close to zero exhibits a smooth crossover.