Universality and Critical Phenomena in String Defect Statistics

TL;DR

This paper investigates the statistical properties of string defects after symmetry-breaking phase transitions, finding potential universality in critical exponents and demonstrating the generic presence of infinite strings across various models and discretizations.

Contribution

The study extends previous work by analyzing defect statistics on a different ground state manifold and explores the universality of critical exponents in string defect networks.

Findings

Critical exponents of the Hagedorn transition are likely universal.

Infinite strings are generically present in all examined models and discretizations.

The improved algorithm enhances statistical analysis of defect networks.

Abstract

The idea of biased symmetries to avoid or alleviate cosmological problems caused by the appearance of some topological defects is familiar in the context of domain walls, where the defect statistics lend themselves naturally to a percolation theory description, and for cosmic strings, where the proportion of infinite strings can be varied or disappear entirely depending on the bias in the symmetry. In this paper we measure the initial configurational statistics of a network of string defects after a symmetry-breaking phase transition with initial bias in the symmetry of the ground state. Using an improved algorithm, which is useful for a more general class of self-interacting walks on an infinite lattice, we extend the work in \cite{MHKS} to better statistics and a different ground state manifold, namely $\R P^2$, and explore various different discretisations. Within the statistical errors, the critical exponents of the Hagedorn transition are found to be quite possibly universal and identical to the critical exponents of three-dimensional bond or site percolation. This improves our understanding of the percolation theory description of defect statistics after a biased phase transition, as proposed in \cite{MHKS}. We also find strong evidence that the existence of infinite strings in the Vachaspati Vilenkin algorithm is generic to all (string-bearing) vacuum manifolds, all discretisations thereof, and all regular three-dimensional lattices.