Statistical Properties of Strings

Abstract

We investigate numerically the configurational statistics of strings. The algorithm models an ensemble of global $U(1)$ cosmic strings, or equivalently vortices in superfluid ${}^4$He. We use a new method which avoids the specification of boundary conditions on the lattice. We therefore do not have the artificial distinction between short and long string loops or a `second phase' in the string network statistics associated with strings winding around a toroidal lattice. Our lattice is also tetrahedral, which avoids ambiguities associated with the cubic lattices of previous work. We find that the percentage of infinite string is somewhat lower than on cubic lattices, 63\% instead of 80\%. We also investigate the Hagedorn transition, at which infinite strings percolate, controlling the string density by rendering one of the equilibrium states more probable. We measure the percolation threshold, the critical exponent associated with the divergence of a suitably defined susceptibility of the string loops, and that associated with the divergence of the correlation length.

20 pages, 8 figures (uuencoded) appended, DAMTP-94-56, SUSX-TP-94-72

References in corpus (3)

• The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals
• Formation of Topological Defects at First Order Phase Transitions
• On the Production of Flux Vortices and Magnetic Monopoles in Phase Transitions

Cited by in corpus (27)

• Evolution of a Non-Abelian Cosmic String Network
• The evolution of a network of cosmic string loops
• Majorana Loop Models for Measurement-Only Quantum Circuits
• Vortex knots in tangled quantum eigenfunctions
• Kertesz Line in the Three-Dimensional Compact U(1) Lattice Higgs Model
• Universal statistics of vortex lines
• Percolation, Bose-Einstein Condensation, and String Proliferation
• Level Set Method for the Evolution of Defect and Brane Networks
• Where are the Hedgehogs in Nematics?
• Geometry and scaling of tangled vortex lines in three-dimensional random wave fields
• "Lattice-Free" Simulations of Topological Defect Formation
• Bubble nucleation and growth in slow cosmological phase transitions
• Quench dynamics of the three-dimensional U(1) complex field theory: geometric and scaling characterisation of the vortex tangle
• Universality and Critical Phenomena in String Defect Statistics
• Phase transitions in diluted negative-weight percolation models
• Cosmic String Formation from Correlated Fields
• On The Absence Of Open Strings In A Lattice-Free Simulation Of Cosmic String Formation
• Cosmic string formation and the power spectrum of field configurations
• Is negative-weight percolation compatible with SLE?
• Mean-field behavior of the negative-weight percolation model on random regular graphs
• An Extension to Models for Cosmic String Formation
• Configurational statistics of densely and fully packed loops in the negative-weight percolation model
• Analysis of the loop length distribution for the negative weight percolation problem in dimensions d=2 through 6
• Universal statistics of vortex tangle in three-dimensional wave chaos
• Metastable cosmic strings are broken at the start
• Random Colorings in Manifolds
• Tricolor percolation and random paths in 3D