Non-Kosterlitz-Thouless transitions for the q-state clock models.

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics

Background:

• The q-state clock model describes systems with discrete rotational symmetry.
• Phase transitions in such models are influenced by the number of states (q) and interaction potentials.

Purpose of the Study:

• To investigate the nature of the high-temperature phase transition in the five-state clock model.
• To understand the influence of interaction potentials on phase transition characteristics.

Main Methods:

• Monte Carlo simulations were employed to study the q-state clock model.
• The helicity modulus was calculated to analyze phase transition properties.

Main Results:

• The five-state clock model's high-temperature transition does not exhibit a vanishing helicity modulus, distinguishing it from Kosterlitz-Thouless (KT) transitions.
• Models with q≥6 show vanishing helicity modulus, consistent with KT transitions.
• Modifying the interaction potential can alter transition types; the KT transition for q=6 becomes non-KT, and the non-KT transition for q=5 reverts to KT with a Villain potential.

Conclusions:

• The transition in the five-state clock model is a distinct non-KT type, driven by the interaction between the number of angular directions and the cosine potential.
• The study highlights the sensitivity of phase transition universality classes to specific model parameters and potentials.