Statistical mechanics of strings with Y-junctions

TL;DR

This paper studies the phase transitions of string networks with Y-junctions, revealing how different string types undergo Hagedorn transitions at various temperatures, affecting the formation of infinite strings and loops.

Contribution

It introduces a simplified model linking string networks with Y-junctions to coupled XY models, providing a detailed phase diagram and insights into their thermal behavior.

Findings

Lightest strings undergo Hagedorn transition first

Existence of a higher critical temperature for infinite strings

At low temperatures, only lightest strings form small loops

Abstract

We investigate the Hagedorn transitions of string networks with Y-junctions as may occur, for example, with (p,q) cosmic superstrings. In a simplified model with three different types of string, the partition function reduces to three generalised coupled XY models. We calculate the phase diagram and show that, as the system is heated, the lightest strings first undergo the Hagedorn transition despite the junctions. There is then a second, higher, critical temperature above which infinite strings of all tensions, and junctions, exist. Conversely, on cooling to low temperatures, only the lightest strings remain, but they collapse into small loops.