Phase Structure and Compactness

TL;DR

This paper compares the phase structures of compact and non-compact two-dimensional multi-frequency sine-Gordon models, revealing that while high-energy behaviors are similar, their low-energy phase transitions differ due to compactness.

Contribution

It demonstrates that compactness affects low-energy phase transitions in multi-frequency sine-Gordon models, while high-energy scaling remains unaffected.

Findings

High-energy scaling is identical for both models.

Compact model exhibits first and second order phase transitions.

Non-compact model lacks these low-energy phase transitions.

Abstract

In order to study the influence of compactness on low-energy properties, we compare the phase structures of the compact and non-compact two-dimensional multi-frequency sine-Gordon models. It is shown that the high-energy scaling of the compact and non-compact models coincides, but their low-energy behaviors differ. The critical frequency $\beta^2 = 8\pi$ at which the sine-Gordon model undergoes a topological phase transition is found to be unaffected by the compactness of the field since it is determined by high-energy scaling laws. However, the compact two-frequency sine-Gordon model has first and second order phase transitions determined by the low-energy scaling: we show that these are absent in the non-compact model.